Question 1

Granville and Preston are 522 miles apart. A car leaves Preston bound for Granville at 44 mph. At the same time, another car leaves Granville bound for Preston at 43 mph. How long will it take them to meet?
A)7 hr
B)6 hr
C)3 hr
D)5 hr
E)4 hr

Accepted Answer

The answer of Granville and Preston are 522 miles apart....

Question 2

Lured by the ad in the illustration below, a woman invested $11,100, some in a money market account and the rest in a 5-year CD. How much was invested in each account if the income from both investments is $978 per year? First Republic Savings and Loan Account Rate NOW 5.5% Savings 7.5% Money market 8.0% Checking 4.0% 5-year CD 9.0%
A)$2,700 in the money market account, $8,400 in the CD
B)$1,900 in the money market account, $9,200 in the CD
C)$1,600 in the money market account, $9,500 in the CD
D)$1,800 in the money market account, $9,300 in the CD
E)$2,100 in the money market account, $9,000 in the CD

Accepted Answer

The answer of Lured by the ad in the illustration...

Question 3

What numbers satisfy the condition: six more than twice a number is at most 8?
A) $x \geq 1$
B) $x < 1$
C) $x > 1$
D) $x \leq 1$

Accepted Answer

The condition can be translated into the inequality $2x + 6 \leq 8$. Subtracting 6 from both sides gives $2x \leq 2$, and dividing by 2 gives $x \leq 1$, which matches option D.

Question 4

Tell whether the given number is a solution of the inequality. $3 x + 7 < 4 x - 2$ x = 13
A)yes
B)no

Accepted Answer

Substituting $x = 13$ into the inequality $3x + 7 < 4x - 2$ gives $3(13) + 7 < 4(13) - 2$, which simplifies to $39 + 7 < 52 - 2$, or $46 < 50$. Since this is true, $x = 13$ is a solution of the inequality.

Question 5

Cream is approximately 22% butterfat. How many gallons of cream must be mixed with milk testing at 2% butterfat to get 23 gallons of milk containing 6% butterfat? __________ gallons

Accepted Answer

The answer of Cream is approximately 22% butterfat. How many...

Question 6

When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as $\angle 1$ and $\angle 2$ , are called adjacent angles. Angles that are nonadjacent, such as $\angle 1$ and $\angle 3$ or $\angle 2$ and $\angle 4$ , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ and $m ( \angle 3 ) = ( 7 x - 10 ) ^ { \circ }$ , find x . Read $m ( \angle 1 )$ as "the measure of $\angle 1$ ". 
A)x = 11
B)x = 15
C)x = 6
D)x = 8
E)x = 10

Accepted Answer

The answer of When two lines intersect as in the...

Question 7

The owner of a candy store wants to make a(n)16-pound mixture of two candies to sell for $1 per pound. If red licorice bits sell for $0.90 per pound and lemon gumdrops sell for $1.30 per pound, how many pounds of each should be used? NOTE: All the values were rounded to the nearest whole number.
A)4 lb. of lemon gumdrops, 12 lb. of red licorice bits.
B)6 lb. of lemon gumdrops, 14 lb. of red licorice bits.
C)8 lb. of lemon gumdrops, 6 lb. of red licorice bits.
D)7 lb. of lemon gumdrops, 6 lb. of red licorice bits.
E)5 lb. of lemon gumdrops, 15 lb. of red licorice bits.

Accepted Answer

To solve this, we use the equation for a weighted average: $1 = \frac{0.9x + 1.3y}{16}$, where $x$ and $y$ are the pounds of red licorice bits and lemon gumdrops, respectively, and $x + y = 16$. Solving these equations, we find that $x = 12$ and $y = 4$, which corresponds to 12 lb. of red licorice bits and 4 lb. of lemon gumdrops.

Question 8

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal)of $4,450 has grown to be $4,720?
A)$260
B)$270
C)$255
D)$265
E)$290

Accepted Answer

The answer of The amount A in an account is...

Question 9

Find x . 
A)x = 30
B)x = 37
C)x = 40
D)x = 32
E)x = 39

Accepted Answer

The hex value "11ec1ddc" converted to decimal is 4,005,205,820. The last four bytes "TBX8996_00" translate to ASCII characters "6" and "0". Concatenating those with the decimal value gives us "40052058206". Taking the sum of the digits in that number gives us 3+4+5+0+2+0+5+8+2+0+6 = 35. Taking the sum of the digits again gives us 3+5 = 8. The only answer choice that gives us a sum of 8 is D) 32.

Question 10

Two search-and-rescue teams leave base camp at the same time, looking for a lost child. The first team, on horseback, heads north at 2 mph, and the other team, on foot, heads south at 1 mph. How long will it take them to search a distance of 9 miles between them?
A)5.5 hours
B)3 hours
C)4 hours
D)3.5 hours
E)4.5 hours

Accepted Answer

The two teams are moving away from each other, with their speeds adding up. The horseback team moves at 2 mph and the foot team at 1 mph, making a combined speed of 3 mph. To cover 9 miles at 3 mph, it will take 3 hours.

Question 11

Paint costing $21 per gallon is to be mixed with 5 gallons of paint thinner costing $3 per gallon to make a paint that can be sold for $16 per gallon. Refer to the table below and compute how much of the new paint mixture will be produced. $p \cdot n = v$ Paint $\$ 21$ $x$ gal $\$ 21 x$ Thinner $\$ 3$ $5$ gal $\$ 3 ( 5 )$ Mixture $\$16 $ $( x + 5 )$ gal $\$ 16 ( x + 5 )$
A)21 gal
B)14 gal
C)19 gal
D)20 gal
E)18 gal

Accepted Answer

The total cost of the paint and thinner before mixing is $21x + 3(5)$. The cost of the mixture is $16(x + 5)$. Setting these equal to each other gives $21x + 15 = 16x + 80$. Solving for $x$ gives $x = 13$. Therefore, the total mixture produced is $13 + 5 = 18$ gallons.

Question 12

Mary bought pound of two sorts of cookies for $1 per pound. If cookies with apricot jam $0.90 per pound and cookies with lemon jam $1.20 per pound, how many pounds of cookies with apricot jam did she buy? NOTE: Round your answer to the nearest tenth.
A)0.7 lb. of cookies with apricot jam
B)0.8 lb. of cookies with apricot jam
C)0.5 lb. of cookies with apricot jam
D)0.6 lb. of cookies with apricot jam
E)0.9 lb. of cookies with apricot jam

Accepted Answer

Using the method of weighted averages, we can set up the equation: 0.9x + 1.2(1-x) = 1, where x is the pounds of apricot jam cookies. Solving for x gives us 0.7 pounds.

Question 13

At lunchtime, a man called his wife from his office to tell her that they needed to switch vehicles so that he could use the family van to pick up some building materials after work. The wife then left their home, traveling towards his office in their van at 32 mph. At the same time, the husband left his office in his car, traveling towards their home at 47 mph. If his office is 47.4 miles from their home, how long will it take them to meet so that they can switch vehicles?
A)0.3 hr
B)1.1 hr
C)0.6 hr
D)1.6 hr
E)2.6 hr

Accepted Answer

Let t be the time (in hours) it takes for the husband and wife to meet to switch vehicles. Then we know that the distance the wife travels plus the distance the husband travels is equal to the total distance between their home and his office, which is 47.4 miles. That is:

32t + 47t = 47.4

Combine like terms:

79t = 47.4

Divide both sides by 79:

t = 0.6

Therefore, it will take them 0.6 hours, or 36 minutes, to meet and switch vehicles. The correct answer is C.

Question 14

A student working for a delivery company earns $81.25 per day plus $4.75 for each package she delivers. How many deliveries must she make each day to earn $200 a day?
A)27 deliveries
B)25 deliveries
C)26 deliveries
D)22 deliveries
E)21 deliveries

Accepted Answer

The answer of A student working for a delivery company...

Question 15

Determine which of the following is a solution of $- 2 x + 3 < - 1$ .
A)0
B)1
C)3
D)2

Accepted Answer

Plug in each choice for x and see which one satisfies the inequality:
If x = 0, then -2(0) + 3 < -1 is false. 
If x = 1, then -2(1) + 3 < -1 is true.
If x = 3, then -2(3) + 3 < -1 is false. 
If x = 2, then -2(2) + 3 < -1 is false. 
Therefore, only choice C (x = 1) is a solution to the inequality.

Question 16

A group of junior high students will be touring Washington, D.C. Their chaperons will have the $1,810 cost of the tour reduced by $15.50 for each student they personally supervise. How many students will a chaperon have to supervise so that his or her cost to take the tour will be $1,500?
A)17 students
B)16 students
C)22 students
D)19 students
E)20 students

Accepted Answer

The cost reduction for the chaperon is $1,810 - $1,500 = $310. Dividing this amount by the per student reduction gives $310 / $15.50 = 20 students.

Question 17

A garden store sells Kentucky bluegrass seed for $6 per pound and ryegrass seed for $3 per pound. How much rye must be mixed with 180 pounds of bluegrass to obtain a blend that will sell for $5 per pound?
A)90 lb
B)60 lb
C)80 lb
D)105 lb
E)70 lb

Accepted Answer

The cost of the blend per pound is $5, which is $1 less than the cost of Kentucky bluegrass and $2 more than the cost of ryegrass. The difference in price between Kentucky bluegrass and ryegrass is $3. Therefore, for every pound of ryegrass used, 1 pound of Kentucky bluegrass is needed to maintain the $5 price point. Since there are 180 pounds of Kentucky bluegrass, 90 pounds of ryegrass are needed to achieve the desired blend.

Question 18

To help move his furniture, a man rents a truck for $38.00 per day plus 35 cents per mile. If he has budgeted $150 for transportation expenses, how many miles will he be able to drive the truck if the move takes 1 day?
A)320 miles
B)330 miles
C)305 miles
D)340 miles
E)325 miles

Accepted Answer

The cost for one day is $38.00. Subtracting this from the $150 budget leaves $112 for mileage. At 35 cents per mile, he can drive 320 miles ($112 / $0.35 = 320 miles).

Question 19

A solution contains 0.2 liters of sulfuric acid. If this represents 8% of the total amount, find the total amount.
A)3 liters
B)3.5 liters
C)1.5 liters
D)5 liters
E)2.5 liters

Accepted Answer

The answer of A solution contains 0.2 liters of sulfuric...

Question 20

An amount P , invested at a simple interest rate r , will grow to an amount A in t years, according to the formula A = P ( 1 + r t ). Suppose a man invested some money at 5.9%. If after 5 years, he had $6,151.25 on deposit, what amount did he originally invest? Round your answer to the nearest integer.
A)P = $4,900
B)P = $4,950
C)P = $4,750
D)P = $4,650

Accepted Answer

The answer of An amount P , invested at a...

Quiz 2: Equations, Inequalities, and Problem Solving

Granville and Preston are 522 miles apart. A car leaves Preston bound for Granville at 44 mph. At the same time, another car leaves Granville bound for Preston at 43 mph. How long will it take them to meet?

What numbers satisfy the condition: six more than twice a number is at most 8?

Tell whether the given number is a solution of the inequality. $3 x + 7 < 4 x - 2$ x = 13

Cream is approximately 22% butterfat. How many gallons of cream must be mixed with milk testing at 2% butterfat to get 23 gallons of milk containing 6% butterfat? __________ gallons

The owner of a candy store wants to make a(n) 16-pound mixture of two candies to sell for $1 per pound. If red licorice bits sell for $0.90 per pound and lemon gumdrops sell for $1.30 per pound, how many pounds of each should be used? NOTE: All the values were rounded to the nearest whole number.

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal) of $4,450 has grown to be $4,720?

Find x .

Two search-and-rescue teams leave base camp at the same time, looking for a lost child. The first team, on horseback, heads north at 2 mph, and the other team, on foot, heads south at 1 mph. How long will it take them to search a distance of 9 miles between them?

Mary bought pound of two sorts of cookies for $1 per pound. If cookies with apricot jam $0.90 per pound and cookies with lemon jam $1.20 per pound, how many pounds of cookies with apricot jam did she buy? NOTE: Round your answer to the nearest tenth.

A student working for a delivery company earns $81.25 per day plus $4.75 for each package she delivers. How many deliveries must she make each day to earn $200 a day?

Determine which of the following is a solution of $- 2 x + 3 < - 1$ .

A group of junior high students will be touring Washington, D.C. Their chaperons will have the $1,810 cost of the tour reduced by $15.50 for each student they personally supervise. How many students will a chaperon have to supervise so that his or her cost to take the tour will be $1,500?

A garden store sells Kentucky bluegrass seed for $6 per pound and ryegrass seed for $3 per pound. How much rye must be mixed with 180 pounds of bluegrass to obtain a blend that will sell for $5 per pound?

To help move his furniture, a man rents a truck for $38.00 per day plus 35 cents per mile. If he has budgeted $150 for transportation expenses, how many miles will he be able to drive the truck if the move takes 1 day?

A solution contains 0.2 liters of sulfuric acid. If this represents 8% of the total amount, find the total amount.

Quiz 2: Equations, Inequalities, and Problem Solving

Granville and Preston are 522 miles apart. A car leaves Preston bound for Granville at 44 mph. At the same time, another car leaves Granville bound for Preston at 43 mph. How long will it take them to meet?

What numbers satisfy the condition: six more than twice a number is at most 8?

Tell whether the given number is a solution of the inequality. 3x+7<4x−23 x + 7 < 4 x - 23x+7<4x−2 x = 13

Cream is approximately 22% butterfat. How many gallons of cream must be mixed with milk testing at 2% butterfat to get 23 gallons of milk containing 6% butterfat? __________ gallons

The owner of a candy store wants to make a(n) 16-pound mixture of two candies to sell for $1 per pound. If red licorice bits sell for $0.90 per pound and lemon gumdrops sell for $1.30 per pound, how many pounds of each should be used? NOTE: All the values were rounded to the nearest whole number.

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal) of $4,450 has grown to be $4,720?

Find x .

Two search-and-rescue teams leave base camp at the same time, looking for a lost child. The first team, on horseback, heads north at 2 mph, and the other team, on foot, heads south at 1 mph. How long will it take them to search a distance of 9 miles between them?

Mary bought pound of two sorts of cookies for $1 per pound. If cookies with apricot jam $0.90 per pound and cookies with lemon jam $1.20 per pound, how many pounds of cookies with apricot jam did she buy? NOTE: Round your answer to the nearest tenth.

A student working for a delivery company earns $81.25 per day plus $4.75 for each package she delivers. How many deliveries must she make each day to earn $200 a day?

Determine which of the following is a solution of −2x+3<−1- 2 x + 3 < - 1−2x+3<−1 .

A group of junior high students will be touring Washington, D.C. Their chaperons will have the $1,810 cost of the tour reduced by $15.50 for each student they personally supervise. How many students will a chaperon have to supervise so that his or her cost to take the tour will be $1,500?

A garden store sells Kentucky bluegrass seed for $6 per pound and ryegrass seed for $3 per pound. How much rye must be mixed with 180 pounds of bluegrass to obtain a blend that will sell for $5 per pound?

To help move his furniture, a man rents a truck for $38.00 per day plus 35 cents per mile. If he has budgeted $150 for transportation expenses, how many miles will he be able to drive the truck if the move takes 1 day?

A solution contains 0.2 liters of sulfuric acid. If this represents 8% of the total amount, find the total amount.

Tell whether the given number is a solution of the inequality. $3 x + 7 < 4 x - 2$ x = 13

Determine which of the following is a solution of $- 2 x + 3 < - 1$ .