Question 1

Solve the problem.
-How much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get an 80% acid solution?

Accepted Answer

The amount of pure acid needed can be found by setting up the equation: $x + 0.50(6) = 0.80(x + 6)$, where $x$ is the amount of pure acid to be added. Solving for $x$ gives $x = 9$ gallons.

Question 2

Solve the problem.
-Mardi received an inheritance of $50,000. She invested part at 1.75% and deposited the remainder in tax-free bonds at 2%. Her total annual income from the investments was $925. Find the amount invested at 1.75%.

Accepted Answer

The answer of Solve the problem.
-Mardi received an inheritance of...

Question 3

Solve the problem.
-Tom Quig traveled 290 miles east of St. Louis. For most of the trip he averaged 70 mph, but for one period of time he was slowed to 20 mph due to a major accident. If the total time of travel was 7 hours, how many miles
Did he drive at the reduced speed?

Accepted Answer

Let x be the distance traveled at 20 mph. Then, the distance traveled at 70 mph is 290 - x. The time for each part of the trip is x/20 and (290-x)/70. The total time is 7 hours: x/20 + (290-x)/70 = 7. Solving this equation gives x = 80 miles.

Question 4

Solve the problem.
-Find the height of a moving box if its length is 30 in., its width is 33 in., and its surface area is $3618 \text { in } ^ { 2 }$ . Assume that the surface area includes the top of the moving box.

Accepted Answer

The surface area $A$ of a box can be calculated using the formula $A = 2lw + 2lh + 2wh$, where $l$ is the length, $w$ is the width, and $h$ is the height. Given $l = 30$ in, $w = 33$ in, and $A = 3618$ in$^2$, we can substitute these values into the formula and solve for $h$. Rearranging the formula to solve for $h$, we get $h = \frac{A - 2lw}{2l + 2w}$. Substituting the given values, we find $h = 13$ in.

Question 5

Solve the problem.
-An airplane flies from Metro City to Gotham with a tailwind that increases its normal speed by 100 mph. On the return trip, the plane must fly against this wind, which decreases its normal speed by the same amount. The
Flight from Metro City takes 2.00 hours and the return trip takes 3.60 hours. How far is it from Metro City to
Gotham?

Accepted Answer

The answer of Solve the problem.
-An airplane flies from Metro...

Question 6

Solve the problem.
-It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 20 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired
Strength?

Accepted Answer

Let x liters of 20% solution be drained and replaced with 100% antifreeze.Then, (20/100) * 20 + (100/100) * x = (40/100) * (20 + x)=> 4 + x = 8 + 0.4x=> 0.6x = 4=> x = 4/0.6 = 6.66 liters (approx.)

Question 7

Solve the problem.
-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 5 miles per hour, and Delvis is traveling at a speed of 10 miles per hour. In 3 hours what is the distance between them (assuming
That they began at the same point and time)?

Accepted Answer

In 3 hours, Candy travels 15 miles (5 mph * 3 hours), and Delvis travels 30 miles (10 mph * 3 hours). The distance between them is 30 miles - 15 miles = 15 miles.

Question 8

Solve the problem.
-Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 250 miles in the same time that Dana travels 230 miles. If Chuck's rate of travel is 4 mph more than Dana's, and they travel the same length of time, at
What speed does Chuck travel?

Accepted Answer

Chuck's speed is 50 mph, derived from the equation system based on distance = rate × time, with Chuck's rate being Dana's rate + 4 mph.

Question 9

Solve the problem.
-Jill is 9 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 kilometers per hour. They meet in 2 hours. How fast is Joe walking?

Accepted Answer

Joe is walking at 3 km/hr because in 2 hours, Jill covers 3 km (1.5 km/hr * 2 hr), so the remaining 6 km (9 km - 3 km) must be covered by Joe in 2 hours, which means Joe walks at 3 km/hr (6 km / 2 hr).

Question 10

Solve the problem.
-Helen Weller invested $12,000 in an account that pays 1.25% simple interest. How much additional money must be invested in an account that pays 3.5% simple interest so that the average return on the two investments
Amounts to 2%?

Accepted Answer

The answer of Solve the problem.
-Helen Weller invested $12,000 in...

Question 11

Solve the problem.
-Noah and Ben are running in the Walker Street Fun Run. Noah runs at 7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are $\frac { 1 } { 5 }$ mile apart?

Accepted Answer

To find out how long it will take for Noah and Ben to be 1/5 mile apart, we calculate the difference in their speeds, which is 7 mph - 5 mph = 2 mph. Since they are getting 2 miles apart every hour, to find out when they will be 1/5 mile apart, we divide 1/5 by 2, which gives us 1/10 of an hour. Converting 1/10 of an hour to minutes (since there are 60 minutes in an hour), we get 60 * 1/10 = 6 minutes.

Question 12

Solve the problem.
-An airplane leaves Los Angeles for Denver at a speed of 450 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 470 mph. When they
Meet, how far are they from Denver?

Accepted Answer

The first plane travels for 0.5 hours before the second plane departs, covering 225 miles (450 mph * 0.5 hours). When the second plane departs, the distance between them is 625 miles (850 - 225). The planes are moving towards each other at a combined speed of 920 mph (450 + 470). They meet after 625/920 hours, during which the second plane travels 319 miles (470 * 625/920).

Question 13

Solve the problem.
-A chemist needs 130 milliliters of a 72% solution but has only 17% and 82% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

The answer of Solve the problem.
-A chemist needs 130 milliliters...

Question 14

Solve the problem.
-From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 11 miles per hour. In how many hours will they be 40 miles apart?

Accepted Answer

The relative speed of the two boats is 9 + 11 = 20 miles per hour. To be 40 miles apart, it will take 40 / 20 = 2 hours.

Question 15

Solve the problem.
-In the morning, May drove to an appointment at 50 mph. Her average speed on the return trip in the afternoon was 40 mph. The return trip took $\frac { 1 } { 8 }$ hour longer. How far did she travel to the appointment?

Accepted Answer

The distance to the appointment can be found using the formula $d = rt$, where $d$ is distance, $r$ is rate, and $t$ is time. Let $t$ be the time it took for the morning trip. The return trip took $t + \frac{1}{8}$ hours. Since distance is the same for both trips, we can set up the equation: $50t = 40(t + \frac{1}{8})$. Solving for $t$ gives $t = \frac{1}{2}$ hour. Substituting $t$ back into $d = rt$ for the morning trip gives $d = 50 \times \frac{1}{2} = 25$ miles.

Question 16

Solve the problem.
-How many liters of a 30% alcohol solution must be mixed with 50 liters of a 90% solution to get a 50% solution?

Accepted Answer

To find the amount of 30% solution needed, set up the equation: 0.3x + 0.9(50) = 0.5(x + 50). Solving for x gives x = 100 liters.

Question 17

Solve the problem.
-On a recent trip, Sarah's car traveled 20 mph faster on the first 110 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Accepted Answer

The speed for the first part of the trip is 58 mph. To solve this, let's denote the speed on the remaining part as x mph. Therefore, the speed on the first part is x + 20 mph. The time to cover the first 110 miles is 110 / (x + 20), and the time to cover the remaining 80 miles is 80 / x. According to the problem, the total time is 4 hours, so we have the equation 110 / (x + 20) + 80 / x = 4. Solving this equation for x gives the speed on the remaining part, and adding 20 to this speed gives the speed on the first part, which is 58 mph.

Question 18

Solve the problem.
-In a chemistry class, 3 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Accepted Answer

To solve the problem, set up the equation based on the concentration of silver iodide:  (3 liters * 4%) + (x liters * 10%) = (3 + x) liters * 6%.  This simplifies to:  0.12 + 0.1x = 0.18 + 0.06x.  Solving for x gives x = 1.5 liters.

Question 19

Solve the problem.
-Walt made an extra $10,000 last year from a part-time job. He invested part of the money at 2% and the rest at 3.25%. He made a total of $237.50 in interest. How much was invested at 3.25%?

Accepted Answer

The answer of Solve the problem.
-Walt made an extra $10,000...

Question 20

Solve the problem.
-Roberto invested some money at 2.5%, and then invested $5000 more than twice this amount at 4%. His total annual income from the two investments was $1565.00. How much was invested at 4%?

Accepted Answer

Let x be the amount invested at 2.5%. Then, the amount invested at 4% is 2x + $5000. The total income from both investments is given by the equation: 0.025x + 0.04(2x + 5000) = 1565. Solving this equation gives x = $13,000, so the amount invested at 4% is 2(13,000) + 5000 = $31,000.

Quiz 2: Equations and Inequalities

Solve the problem. -How much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get an 80% acid solution?

Solve the problem. -Mardi received an inheritance of $50,000. She invested part at 1.75% and deposited the remainder in tax-free bonds at 2%. Her total annual income from the investments was $925. Find the amount invested at 1.75%.

Solve the problem. -Tom Quig traveled 290 miles east of St. Louis. For most of the trip he averaged 70 mph, but for one period of time he was slowed to 20 mph due to a major accident. If the total time of travel was 7 hours, how many miles Did he drive at the reduced speed?

Solve the problem. -Find the height of a moving box if its length is 30 in., its width is 33 in., and its surface area is $3618 \text { in } ^ { 2 }$ . Assume that the surface area includes the top of the moving box.

Solve the problem. -It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 20 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired Strength?

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 5 miles per hour, and Delvis is traveling at a speed of 10 miles per hour. In 3 hours what is the distance between them (assuming That they began at the same point and time) ?

Solve the problem. -Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 250 miles in the same time that Dana travels 230 miles. If Chuck's rate of travel is 4 mph more than Dana's, and they travel the same length of time, at What speed does Chuck travel?

Solve the problem. -Jill is 9 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 kilometers per hour. They meet in 2 hours. How fast is Joe walking?

Solve the problem. -Helen Weller invested $12,000 in an account that pays 1.25% simple interest. How much additional money must be invested in an account that pays 3.5% simple interest so that the average return on the two investments Amounts to 2%?

Solve the problem. -Noah and Ben are running in the Walker Street Fun Run. Noah runs at 7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are $\frac { 1 } { 5 }$ mile apart?

Solve the problem. -An airplane leaves Los Angeles for Denver at a speed of 450 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 470 mph. When they Meet, how far are they from Denver?

Solve the problem. -A chemist needs 130 milliliters of a 72% solution but has only 17% and 82% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 11 miles per hour. In how many hours will they be 40 miles apart?

Solve the problem. -In the morning, May drove to an appointment at 50 mph. Her average speed on the return trip in the afternoon was 40 mph. The return trip took $\frac { 1 } { 8 }$ hour longer. How far did she travel to the appointment?

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 50 liters of a 90% solution to get a 50% solution?

Solve the problem. -On a recent trip, Sarah's car traveled 20 mph faster on the first 110 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Solve the problem. -In a chemistry class, 3 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Solve the problem. -Walt made an extra $10,000 last year from a part-time job. He invested part of the money at 2% and the rest at 3.25%. He made a total of $237.50 in interest. How much was invested at 3.25%?

Solve the problem. -Roberto invested some money at 2.5%, and then invested $5000 more than twice this amount at 4%. His total annual income from the two investments was $1565.00. How much was invested at 4%?