Question 1

To promote sales, a free 5-ounce bottle of shampoo is packaged with every large bottle (see illustration). Use the information on the package to determine how many ounces of shampoo the large bottle contains.  __________ oz

Accepted Answer

The answer of To promote sales, a free 5-ounce bottle...

Question 2

Match between columns
                        Premises: 5( y - 4)- y = 4( y - 5)

Accepted Answer

The Answer of identity equation and impossible equation is...

Question 3

Find the number of gallons of sulfuric acid in 50 gallons of solution in a tank, if the percent of sulfuric acid is 50%.
A)25 gal
B)4.5 gal
C)9 gal
D)18 gal
E)50 gal

Accepted Answer

To find the number of gallons of sulfuric acid in the solution, multiply the total volume of the solution by the percentage of sulfuric acid (expressed as a decimal). Here, 50 gallons * 50% = 50 * 0.5 = 25 gallons.

Question 4

An art gallery displays paintings for artists and receives a commission from the artist when a painting is sold. What is the commission rate if a gallery received $171.70 when a painting was sold for $1,010.00? __________ %

Accepted Answer

The answer of An art gallery displays paintings for artists...

Question 5

Change 0.64 to a percent.
A)0.0064%
B)0.064%
C)6.4%
D)64%
E)none of these

Accepted Answer

To convert a decimal to a percent, you multiply the decimal by 100. So, 0.64 * 100 = 64%.

Question 6

Solve the equation. $$\frac { 9 n } { 10 } - \frac { n } { 12 } = \frac { - 392 } { 60 }$$
A)n = -8
B)n = -14
C)n = 8
D)n = 10
E)n = -11

Accepted Answer

To solve the equation, first find a common denominator for the fractions, which is 60. Convert each fraction to have this common denominator: $$\frac{9n}{10} \times \frac{6}{6} = \frac{54n}{60}$$ $$\frac{n}{12} \times \frac{5}{5} = \frac{5n}{60}$$ The equation becomes: $$\frac{54n}{60} - \frac{5n}{60} = \frac{-392}{60}$$ Simplify the left side by combining like terms: $$\frac{49n}{60} = \frac{-392}{60}$$ Multiply both sides by 60 to get rid of the denominator: $$49n = -392$$ Divide both sides by 49 to solve for n: $$n = \frac{-392}{49} = -8$$

Question 7

Solve the equation. $$\frac { y } { 5 } + \frac { y - 102 } { 6 } = \frac { 3 y + 6 } { 3 }$$
A)y = -5
B)y = -6
C)y = -29
D)y = -32
E)y = -30

Accepted Answer

To solve the equation, first find a common denominator for the fractions, which is 30. Multiply each term by 30 to eliminate the fractions:  $$ 6y + 5(y - 102) = 10(3y + 6) $$  Simplify and solve for y:  $$ 6y + 5y - 510 = 30y + 60 $$  $$ 11y - 510 = 30y + 60 $$  $$ -510 - 60 = 30y - 11y $$  $$ -570 = 19y $$  $$ y = -30 $$

Question 8

Match between columns
                        Premises: 12( x + 4)- 6 x = 6( x + 9)

Accepted Answer

The Answer of identity equation and impossible equation is...

Question 9

$63$ is $33 \frac { 1 } { 3 } \%$ of what number?
A)94.5
B)1,890
C)567
D)189
E)378

Accepted Answer

The answer of $63$ is \(33 \frac { 1 }...

Question 10

30 is what percent of 300?
A)2%
B)1%
C)20%
D)100%
E)10%

Accepted Answer

To find what percent 30 is of 300, you divide 30 by 300 and then multiply by 100. $ \frac{30}{300} \times 100 = 10\%$.

Question 11

After selling a house for $82,000, a real estate agent split the 6% commission with another agent. How much did each person receive? $__________

Accepted Answer

The answer of After selling a house for $82,000, a...

Question 12

What number is 77% of 100?
A)87
B)7,700
C)77
D)177
E)38.5

Accepted Answer

77% of 100 is calculated as (77/100) * 100 = 77.

Question 13

Solve the equation. $$\frac { 3 a - 3 } { 6 } + \frac { 6 a - 6 } { 6 } + \frac { 4 a + 12 } { 8 } = 10$$
A)a = 10
B)a = -5
C)a = 2
D)a = 5
E)a = 8

Accepted Answer

Combine the fractions and simplify the equation to find that $ a = 5 $.

Question 14

Solve the equation. If it is an identity or an impossible equation, so indicate. $$\frac { 5 ( x - 9 ) } { 10 } - \frac { - 75 x } { 50 } = \frac { 10 ( x + 11 ) } { 5 }$$
A)equation has one solution
B)identity equation
C)impossible equation

Accepted Answer

Simplifying both sides of the equation results in a contradiction, indicating that the equation is impossible.

Question 15

If a woman making $30,000 a year receives a cost-of-living increase of 2.6%, how much is her raise? $__________

Accepted Answer

The answer of If a woman making $30,000 a year...

Question 16

Change the following percent to a decimal. 0.4%
A)40
B)0.0004
C)0.4
D)0.04
E)0.004

Accepted Answer

To convert a percent to a decimal, divide by 100. Thus, 0.4% = 0.4/100 = 0.004.

Question 17

Solve the equation. If it is an identity or an impossible equation, so indicate. 8 ( y - 7 )- y = 7 ( y - 8 )
A)impossible equation
B)identity equation
C)equation has one solution

Accepted Answer

Distribute and simplify to obtain 0 = 0, which is an identity.

Question 18

A salesperson for a medical supplies company is paid a commission of 6% for orders under $9,000. For orders exceeding $9,000, she receives an additional 1% in commission on the total amount. What is her commission on a sale of $12,300? $__________

Accepted Answer

The answer of A salesperson for a medical supplies company...

Question 19

The cost to repair a car after a collision was $2,400. The automobile insurance policy paid the entire bill except for a $120 deductible, which the driver paid. What percent of the cost did he pay? __________ %

Accepted Answer

The answer of The cost to repair a car after...

Question 20

Change 6 to a percent.
A)600%
B)0.06%
C)60%
D)0.6%
E)none of these

Accepted Answer

The answer of Change 6 to a percent.
A)600%
B)0.06%
C)60%
D)0.6%
E)none of these...

Quiz 2: Equations, Inequalities, and Problem Solving

To promote sales, a free 5-ounce bottle of shampoo is packaged with every large bottle (see illustration). Use the information on the package to determine how many ounces of shampoo the large bottle contains. __________ oz

Match each equation below with the corresponding type of equation.

Find the number of gallons of sulfuric acid in 50 gallons of solution in a tank, if the percent of sulfuric acid is 50%.

An art gallery displays paintings for artists and receives a commission from the artist when a painting is sold. What is the commission rate if a gallery received $171.70 when a painting was sold for $1,010.00? __________ %

Change 0.64 to a percent.

Solve the equation. $\frac { 9 n } { 10 } - \frac { n } { 12 } = \frac { - 392 } { 60 }$

Solve the equation. $\frac { y } { 5 } + \frac { y - 102 } { 6 } = \frac { 3 y + 6 } { 3 }$

Match each equation below with the corresponding type of equation.

$63$ is $33 \frac { 1 } { 3 } \%$ of what number?

30 is what percent of 300?

After selling a house for $82,000, a real estate agent split the 6% commission with another agent. How much did each person receive? $__________

What number is 77% of 100?

Solve the equation. $\frac { 3 a - 3 } { 6 } + \frac { 6 a - 6 } { 6 } + \frac { 4 a + 12 } { 8 } = 10$

Solve the equation. If it is an identity or an impossible equation, so indicate. $\frac { 5 ( x - 9 ) } { 10 } - \frac { - 75 x } { 50 } = \frac { 10 ( x + 11 ) } { 5 }$

If a woman making $30,000 a year receives a cost-of-living increase of 2.6%, how much is her raise? $__________

Change the following percent to a decimal. 0.4%

Solve the equation. If it is an identity or an impossible equation, so indicate. 8 ( y - 7 ) - y = 7 ( y - 8 )

A salesperson for a medical supplies company is paid a commission of 6% for orders under $9,000. For orders exceeding $9,000, she receives an additional 1% in commission on the total amount. What is her commission on a sale of $12,300? $__________

The cost to repair a car after a collision was $2,400. The automobile insurance policy paid the entire bill except for a $120 deductible, which the driver paid. What percent of the cost did he pay? __________ %

Change 6 to a percent.

Quiz 2: Equations, Inequalities, and Problem Solving

To promote sales, a free 5-ounce bottle of shampoo is packaged with every large bottle (see illustration). Use the information on the package to determine how many ounces of shampoo the large bottle contains. __________ oz

Match each equation below with the corresponding type of equation.

Find the number of gallons of sulfuric acid in 50 gallons of solution in a tank, if the percent of sulfuric acid is 50%.

An art gallery displays paintings for artists and receives a commission from the artist when a painting is sold. What is the commission rate if a gallery received $171.70 when a painting was sold for $1,010.00? __________ %

Change 0.64 to a percent.

Solve the equation. 9n10−n12=−39260\frac { 9 n } { 10 } - \frac { n } { 12 } = \frac { - 392 } { 60 }109n​−12n​=60−392​

Solve the equation. y5+y−1026=3y+63\frac { y } { 5 } + \frac { y - 102 } { 6 } = \frac { 3 y + 6 } { 3 }5y​+6y−102​=33y+6​

Match each equation below with the corresponding type of equation.

636363 is 3313%33 \frac { 1 } { 3 } \%3331​% of what number?

30 is what percent of 300?

After selling a house for $82,000, a real estate agent split the 6% commission with another agent. How much did each person receive? $__________

What number is 77% of 100?

Solve the equation. 3a−36+6a−66+4a+128=10\frac { 3 a - 3 } { 6 } + \frac { 6 a - 6 } { 6 } + \frac { 4 a + 12 } { 8 } = 1063a−3​+66a−6​+84a+12​=10

Solve the equation. If it is an identity or an impossible equation, so indicate. 5(x−9) 10−−75x50=10(x+11) 5\frac { 5 ( x - 9 ) } { 10 } - \frac { - 75 x } { 50 } = \frac { 10 ( x + 11 ) } { 5 }105(x−9) ​−50−75x​=510(x+11) ​

If a woman making $30,000 a year receives a cost-of-living increase of 2.6%, how much is her raise? $__________

Change the following percent to a decimal. 0.4%

Solve the equation. If it is an identity or an impossible equation, so indicate. 8 ( y - 7 ) - y = 7 ( y - 8 )

A salesperson for a medical supplies company is paid a commission of 6% for orders under $9,000. For orders exceeding $9,000, she receives an additional 1% in commission on the total amount. What is her commission on a sale of $12,300? $__________

The cost to repair a car after a collision was $2,400. The automobile insurance policy paid the entire bill except for a $120 deductible, which the driver paid. What percent of the cost did he pay? __________ %

Change 6 to a percent.

Solve the equation. $\frac { 9 n } { 10 } - \frac { n } { 12 } = \frac { - 392 } { 60 }$

Solve the equation. $\frac { y } { 5 } + \frac { y - 102 } { 6 } = \frac { 3 y + 6 } { 3 }$

$63$ is $33 \frac { 1 } { 3 } \%$ of what number?

Solve the equation. $\frac { 3 a - 3 } { 6 } + \frac { 6 a - 6 } { 6 } + \frac { 4 a + 12 } { 8 } = 10$

Solve the equation. If it is an identity or an impossible equation, so indicate. $\frac { 5 ( x - 9 ) } { 10 } - \frac { - 75 x } { 50 } = \frac { 10 ( x + 11 ) } { 5 }$