Question 1

Solve the problem.
-Anne and Nancy use a metal alloy that is 16% copper to make jewelry. How many ounces of an alloy that is 10% copper must be mixed with an alloy that is 20% copper to form 55 ounces of the desired alloy?

Accepted Answer

To find the amount of 10% copper alloy needed, let x be the ounces of 10% alloy. Then, 55 - x will be the ounces of 20% alloy. The equation is 0.10x + 0.20(55 - x) = 0.16(55). Solving this gives x = 22 ounces.

Question 2

Solve the problem.
-How many liters of a 20% alcohol solution must be mixed with 90 liters of a 80% solution to get a 40% solution?

Accepted Answer

To solve this, we use the equation for mixture problems: (amount of first solution * its percentage + amount of second solution * its percentage) / total amount of solution = desired percentage. Let x be the amount of 20% solution needed. The equation is: (0.20x + 0.80*90) / (x + 90) = 0.40. Solving for x gives x = 180 liters.

Question 3

Solve the problem.
-Mardi received an inheritance of $60,000. She invested part at 8% and deposited the remainder in tax-free bonds at 11%. Her total annual income from the investments was $5700. Find the amount invested at 8%.

Accepted Answer

Let the amount invested at 8% be x dollars. Therefore, the amount invested at 11% is $60,000 - x. The total annual income from these investments is given by 0.08x (from the 8% investment) + 0.11($60,000 - x) (from the 11% investment) = $5700. Solving this equation for x gives x = $30,000, which is the amount invested at 8%.

Question 4

Solve.
-A cruise boat travels 48 miles downstream in 3 hours and returns to its starting point upstream in 12 hours. Find the speed of the stream.

Accepted Answer

The speed of the stream is found by first determining the boat's speed in still water and the effect of the current on its speed. The downstream speed is 48 miles / 3 hours = 16 mph, and the upstream speed is 48 miles / 12 hours = 4 mph. The speed of the stream is the difference between the boat's speed in still water and its speed with the current, divided by 2. Thus, (16 mph - 4 mph) / 2 = 6 mph.

Question 5

Solve the problem using the elimination method.
-In a basketball game, Will scored 40 points, consisting only of three-point shots and two-point shots. He made a total of 17 shots. How many shots of each type did he make?

Accepted Answer

Let x be the number of two-point shots and y be the number of three-point shots.From the given information, we have:x + y = 17 (total number of shots)2x + 3y = 40 (total points scored)Solving these equations by elimination, we get:x = 11y = 6Therefore, Will made 11 two-point shots and 6 three-point shots.

Question 6

Solve the problem using the elimination method.
-The sum of two numbers is 41. The larger number minus the smaller number is 9. What are the numbers?

Accepted Answer

The equations are x + y = 41 and x - y = 9. Adding these gives 2x = 50, so x = 25. Substituting x = 25 into x + y = 41 gives y = 16.

Question 7

Solve the problem.
-Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 28 pounds of feed worth $0.62 per pound by mixing one kind worth $0.15 per pound with another worth $0.97 per pound. How many pounds of
The cheaper kind should they use in the mix?

Accepted Answer

The answer of Solve the problem.
-Tim and Judy mix two...

Question 8

Solve the problem.
-Walt made an extra $10,000 last year from a part-time job. He invested part of the money at 10% and the rest at 9%. He made a total of $960 in interest. How much was invested at 9%?

Accepted Answer

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

Question 9

Solve the problem using the elimination method.
-The sum of two numbers is 100. The second number is three times as large as the first number. What are the numbers?

Accepted Answer

The system of equations based on the problem is: x + y = 100 (where x is the first number and y is the second number) and y = 3x. Substituting the second equation into the first gives x + 3x = 100, leading to 4x = 100, so x = 25. Then, y = 3(25) = 75. Therefore, the numbers are 25 and 75.

Question 10

Solve the problem.
-A woman made a deposit of $267. If her deposit consisted of 91 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

Accepted Answer

The answer of Solve the problem.
-A woman made a deposit...

Question 11

Solve the problem.
-A sum of money amounting to $3.45 consists of dimes and quarters. If there are 18 coins in all, how many are quarters?

Accepted Answer

There are 11 quarters because 11 quarters is equal to $2.75 and 18 dimes is equal to $1.80. $2.75 + $1.80 = $4.55.

Question 12

Solve the problem using the elimination method.
-The sum of two numbers is 4. Three times the larger number plus two times the smaller number is 37. Find the numbers.

Accepted Answer

Let the two numbers be x (larger) and y (smaller). The system of equations based on the given information is:1) x + y = 42) 3x + 2y = 37To solve by elimination, multiply the first equation by 2 to align the coefficients of y:2(x + y) = 2(4) => 2x + 2y = 8Now, subtract this new equation from the second equation to eliminate y:(3x + 2y) - (2x + 2y) = 37 - 8x = 29Substitute x = 29 into the first equation to find y:29 + y = 4 => y = 4 - 29 => y = -25Therefore, the numbers are 29 and -25.

Question 13

Solve the problem.
-Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $3.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 25 tickets was $120.00, how many did Ron sell?

Accepted Answer

The answer of Solve the problem.
-Ron and Kathy are ticket-sellers...

Question 14

Solve the problem.
-A merchant has coffee worth $20 a pound that she wishes to mix with 90 pounds of coffee worth $90 a pound to get a mixture that can be sold for $80 a pound. How many pounds of the $20 coffee should be used?

Accepted Answer

The answer of Solve the problem.
-A merchant has coffee worth...

Question 15

Solve the problem.
-There were 670 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $1020. How many adults and how many children attended?

Accepted Answer

Let the number of adults be A and the number of children be C. We have two equations: A + C = 670 (total number of people) and 2A + C = 1020 (total admission receipts, with adults paying $2 and children $1). Solving these equations simultaneously, we find A = 350 and C = 320.

Question 16

Solve the problem.
-Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 28 coins with a total face value of $5.00, how many of the coins are nickels?

Accepted Answer

Let the number of nickels be $n$ and the number of quarters be $q$. We have two equations: $n + q = 28$ (total coins) and $0.05n + 0.25q = 5.00$ (total value). Solving these equations simultaneously, we find $n = 10$ and $q = 18$, so there are 10 nickels.

Question 17

Solve the problem.
-A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 9% cement should he mix with 10 bags of 10.8% cement to produce a mix containing 10% cement?

Accepted Answer

The answer of Solve the problem.
-A contractor mixes concrete from...

Question 18

Solve the problem.
-Ellen wishes to mix candy worth $1.79 per pound with candy worth $3.75 per pound to form 22 pounds of a mixture worth $2.95 per pound. How many pounds of the more expensive candy should she use?

Accepted Answer

To find the amount of the more expensive candy, set up the equation: 1.79x + 3.75(22-x) = 2.95(22). Solving for x gives x = 13 pounds.

Question 19

Solve the problem.
-In a chemistry class, 6 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

The answer of Solve the problem.
-In a chemistry class, 6...

Question 20

Solve the problem.
-Andy has 33 coins made up of quarters and half dollars, and their total value is $13.25. How many quarters does he have?

Accepted Answer

The answer of Solve the problem.
-Andy has 33 coins made...

Quiz 9: Systems of Equations

Solve the problem. -Anne and Nancy use a metal alloy that is 16% copper to make jewelry. How many ounces of an alloy that is 10% copper must be mixed with an alloy that is 20% copper to form 55 ounces of the desired alloy?

Solve the problem. -How many liters of a 20% alcohol solution must be mixed with 90 liters of a 80% solution to get a 40% solution?

Solve the problem. -Mardi received an inheritance of $60,000. She invested part at 8% and deposited the remainder in tax-free bonds at 11%. Her total annual income from the investments was $5700. Find the amount invested at 8%.

Solve. -A cruise boat travels 48 miles downstream in 3 hours and returns to its starting point upstream in 12 hours. Find the speed of the stream.

Solve the problem using the elimination method. -In a basketball game, Will scored 40 points, consisting only of three-point shots and two-point shots. He made a total of 17 shots. How many shots of each type did he make?

Solve the problem using the elimination method. -The sum of two numbers is 41. The larger number minus the smaller number is 9. What are the numbers?

Solve the problem. -Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 28 pounds of feed worth $0.62 per pound by mixing one kind worth $0.15 per pound with another worth $0.97 per pound. How many pounds of The cheaper kind should they use in the mix?

Solve the problem. -Walt made an extra $10,000 last year from a part-time job. He invested part of the money at 10% and the rest at 9%. He made a total of $960 in interest. How much was invested at 9%?

Solve the problem using the elimination method. -The sum of two numbers is 100. The second number is three times as large as the first number. What are the numbers?

Solve the problem. -A woman made a deposit of $267. If her deposit consisted of 91 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

Solve the problem. -A sum of money amounting to $3.45 consists of dimes and quarters. If there are 18 coins in all, how many are quarters?

Solve the problem using the elimination method. -The sum of two numbers is 4. Three times the larger number plus two times the smaller number is 37. Find the numbers.

Solve the problem. -Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $3.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 25 tickets was $120.00, how many did Ron sell?

Solve the problem. -A merchant has coffee worth $20 a pound that she wishes to mix with 90 pounds of coffee worth $90 a pound to get a mixture that can be sold for $80 a pound. How many pounds of the $20 coffee should be used?

Solve the problem. -There were 670 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $1020. How many adults and how many children attended?

Solve the problem. -Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 28 coins with a total face value of $5.00, how many of the coins are nickels?

Solve the problem. -A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 9% cement should he mix with 10 bags of 10.8% cement to produce a mix containing 10% cement?

Solve the problem. -Ellen wishes to mix candy worth $1.79 per pound with candy worth $3.75 per pound to form 22 pounds of a mixture worth $2.95 per pound. How many pounds of the more expensive candy should she use?

Solve the problem. -In a chemistry class, 6 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. -Andy has 33 coins made up of quarters and half dollars, and their total value is $13.25. How many quarters does he have?