Question 1

Solve the problem.
-Walt made an extra $7000 last year from a part-time job. He invested part of the money at 6% and the rest at 8%. He made a total of $480 in interest. How much was invested at 8%?

Accepted Answer

Let x be the amount invested at 8%. Then, the amount invested at 6% is $7000 - x. The total interest from both investments is given by the equation: 0.06(7000 - x) + 0.08x = 480. Solving this equation, we find x = $3000.

Question 2

Solve the problem.
-Ellen wishes to mix candy worth $1.57 per pound with candy worth $3.69 per pound to form 26 pounds of a mixture worth $3.04 per pound. How many pounds of the more expensive candy should she use?

Accepted Answer

To solve this problem, we can use the concept of weighted averages. Let $x$ be the amount of the more expensive candy ($3.69 per pound) that Ellen uses, and $26 - x$ will then be the amount of the cheaper candy ($1.57 per pound). The total cost of the mixture can be represented as $3.69x + 1.57(26 - x)$, and this should equal the total cost of the final mixture, which is $3.04 \times 26$. Setting up the equation:$$3.69x + 1.57(26 - x) = 3.04 \times 26$$Solving this equation for $x$ gives the amount of the more expensive candy needed. Simplifying and solving for $x$ yields:$$3.69x + 40.82 - 1.57x = 79.04$$$$2.12x = 38.22$$$$x = 18$$Therefore, Ellen should use 18 pounds of the more expensive candy.

Question 3

Solve the problem.
-A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 3% cement should he mix with 8 bags of 11% cement to produce a mix containing 7% cement?

Accepted Answer

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

Question 4

Solve the problem.
-Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 19 pounds of feed worth $0.76 per pound by mixing one kind worth $0.41 per pound with another worth $0.96 per pound. How many pounds of The cheaper kind should they use in the mix?

Accepted Answer

To solve this problem, we can use the concept of weighted averages. Let $ x $ be the amount of the cheaper feed ($0.41 per pound) and $ 19 - x $ be the amount of the more expensive feed ($0.96 per pound). The total cost of the mix should equal the cost of the individual parts, so we set up the equation:$$ 0.41x + 0.96(19 - x) = 0.76 \times 19 $$Solving for $ x $:$$ 0.41x + 18.24 - 0.96x = 14.44 $$$$ -0.55x = -3.8 $$$$ x = \frac{-3.8}{-0.55} = 6.909 $$Rounding to the nearest whole number, we get 7 pounds.

Question 5

Solve the problem using the elimination method.
-A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $6.50. Another customer buys 5 hot dogs and 3 bags of potato chips for $14.25. Find the cost of each item.

Accepted Answer

Let the cost of a hot dog be $x$ and the cost of a bag of potato chips be $y$. The system of equations based on the given information is:$$2x + 2y = 6.50$$$$5x + 3y = 14.25$$Multiplying the first equation by 1.5 gives:$$3x + 3y = 9.75$$Subtracting the second equation from this result gives:$$-2x = -4.50$$Solving for $x$ gives $x = 2.25$. Substituting $x = 2.25$ into the first equation and solving for $y$ gives $y = 1.00$.

Question 6

Solve the problem.
-Anne and Nancy use a metal alloy that is 17% copper to make jewelry. How many ounces of an alloy that is 11% copper must be mixed with an alloy that is 22% copper to form 55 ounces of the desired alloy?

Accepted Answer

The answer of Solve the problem.
-Anne and Nancy use a...

Question 7

Solve the problem using the elimination method.
-The sum of two numbers is 8. Three times the larger number plus four times the smaller number is 18. Find the numbers.

Accepted Answer

The answer of Solve the problem using the elimination method.
-The...

Question 8

Solve the problem.
-A sum of money amounting to $4.15 consists of dimes and quarters. If there are 28 coins in all, how many are quarters?

Accepted Answer

Let the number of quarters be q and the number of dimes be d. We have two equations: q + d = 28 and 0.25q + 0.10d = 4.15. Solving these equations, we find q = 9.

Question 9

Solve the problem.
-Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 30 coins with a total face value of $4.90, 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: $n + q = 30$ (total coins) and $0.05n + 0.25q = 4.90$ (total value). Solving these equations simultaneously, we find $n = 13$ and $q = 17$, so there are 13 nickels.

Question 10

Solve the problem.
-How many liters of a 10% alcohol solution must be mixed with 90 liters of a 70% solution to get a 60% solution?

Accepted Answer

To find the amount of 10% solution needed, set up the equation: 0.10x + 0.70(90) = 0.60(x + 90). Solving for x gives x = 18 liters.

Question 11

Solve the problem.
-There were 520 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $1180. How many adults and how many children attended?

Accepted Answer

The system of equations based on the given information is: $3a + 1c = 1180$ and $a + c = 520$, where $a$ is the number of adults and $c$ is the number of children. Solving this system, we find that there were 330 adults and 190 children.

Question 12

Solve the problem.
-A merchant has coffee worth $20 a pound that she wishes to mix with 30 pounds of coffee worth $90 a pound to get a mixture that can be sold for $50 a pound. How many pounds of the $20 coffee should be used?

Accepted Answer

The problem can be solved using the concept of weighted averages or the mixture rule. Let x be the amount of $20 coffee. The total value of the $20 coffee is 20x dollars, and the total value of the $90 coffee is 30*90 = 2700 dollars. The mixture's total value is (x + 30) pounds at $50 per pound, which equals 50(x + 30) dollars. Setting the total values equal gives the equation: 20x + 2700 = 50(x + 30). Solving for x gives x = 40 pounds.

Question 13

Solve the problem.
-A woman made a deposit of $341. If her deposit consisted of 101 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

Accepted Answer

Let x be the number of one-dollar bills. Then the number of five-dollar bills is 101 - x. The total value of the deposit is 1 * x + 5 * (101 - x) = 341. Solving for x gives x = 41.

Question 14

Solve the problem using the elimination method.
-The sum of two numbers is 33. The larger number minus the smaller number is 9. What are the numbers?

Accepted Answer

Let the two numbers be x (larger) and y (smaller). The system of equations based on the given information is: x + y = 33 (sum of the numbers) and x - y = 9 (difference between the numbers). Adding these two equations eliminates y, giving 2x = 42, so x = 21. Substituting x = 21 into one of the original equations gives y = 12. Therefore, the numbers are 21 and 12.

Question 15

Solve the problem.
-Andy has 17 coins made up of quarters and half dollars, and their total value is $4.75. How many quarters does he have?

Accepted Answer

The total value of the coins is $4.75. Let's denote the number of quarters as Q and the number of half dollars as H. We have two equations: Q + H = 17 (since there are 17 coins in total) and 0.25Q + 0.5H = 4.75 (since the total value of the coins is $4.75). Solving these equations simultaneously, we find that Q = 15, meaning Andy has 15 quarters.

Question 16

Solve the problem using the elimination method.
-The sum of two numbers is 96. The second number is three times as large as the first number. What are the numbers?

Accepted Answer

Let the first number be x and the second number be 3x. The equation based on the given information is x + 3x = 96. Solving this equation, we get 4x = 96, so x = 24. Therefore, the first number is 24, and the second number is 3*24 = 72.

Question 17

Solve the problem.
-Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 26 tickets was $118.50, how many did Ron sell?

Accepted Answer

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

Question 18

Solve the problem using the elimination method.
-In a basketball game, Will scored 35 points, consisting only of three-point shots and two-point shots. He made a total of 15 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. We have two equations: x + y = 15 (total shots) and 2x + 3y = 35 (total points). Solving these equations using the elimination method, we find x = 10 and y = 5.

Question 19

Solve the problem.
-Mardi received an inheritance of $70,000. She invested part at 10% and deposited the remainder in tax-free bonds at 8%. Her total annual income from the investments was $6200. Find the amount invested at 10%.

Accepted Answer

Mardi invested $30,000 at 10% to earn a total of $6200 annually, with the rest at 8%. This is determined by setting up the equation 0.10x + 0.08(70,000 - x) = 6,200, where x is the amount invested at 10%. Solving for x gives $30,000.

Question 20

Solve the problem.
-In a chemistry class, 9 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 find the amount of 10% solution needed, set up the equation: 0.04(9) + 0.10(x) = 0.06(9 + x). Solving for x gives x = 4.5 L.

Quiz 8: Systems of Equations

Solve the problem. -Walt made an extra $7000 last year from a part-time job. He invested part of the money at 6% and the rest at 8%. He made a total of $480 in interest. How much was invested at 8%?

Solve the problem. -Ellen wishes to mix candy worth $1.57 per pound with candy worth $3.69 per pound to form 26 pounds of a mixture worth $3.04 per pound. How many pounds of the more expensive candy should she use?

Solve the problem. -A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 3% cement should he mix with 8 bags of 11% cement to produce a mix containing 7% cement?

Solve the problem. -Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 19 pounds of feed worth $0.76 per pound by mixing one kind worth $0.41 per pound with another worth $0.96 per pound. How many pounds of The cheaper kind should they use in the mix?

Solve the problem using the elimination method. -A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $6.50. Another customer buys 5 hot dogs and 3 bags of potato chips for $14.25. Find the cost of each item.

Solve the problem. -Anne and Nancy use a metal alloy that is 17% copper to make jewelry. How many ounces of an alloy that is 11% copper must be mixed with an alloy that is 22% copper to form 55 ounces of the desired alloy?

Solve the problem using the elimination method. -The sum of two numbers is 8. Three times the larger number plus four times the smaller number is 18. Find the numbers.

Solve the problem. -A sum of money amounting to $4.15 consists of dimes and quarters. If there are 28 coins in all, how many are quarters?

Solve the problem. -Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 30 coins with a total face value of $4.90, how many of the coins are nickels?

Solve the problem. -How many liters of a 10% alcohol solution must be mixed with 90 liters of a 70% solution to get a 60% solution?

Solve the problem. -There were 520 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $1180. How many adults and how many children attended?

Solve the problem. -A merchant has coffee worth $20 a pound that she wishes to mix with 30 pounds of coffee worth $90 a pound to get a mixture that can be sold for $50 a pound. How many pounds of the $20 coffee should be used?

Solve the problem. -A woman made a deposit of $341. If her deposit consisted of 101 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 using the elimination method. -The sum of two numbers is 33. The larger number minus the smaller number is 9. What are the numbers?

Solve the problem. -Andy has 17 coins made up of quarters and half dollars, and their total value is $4.75. How many quarters does he have?

Solve the problem using the elimination method. -The sum of two numbers is 96. The second number is three times as large as the first number. What are the numbers?

Solve the problem. -Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 26 tickets was $118.50, how many did Ron sell?

Solve the problem using the elimination method. -In a basketball game, Will scored 35 points, consisting only of three-point shots and two-point shots. He made a total of 15 shots. How many shots of each type did he make?

Solve the problem. -Mardi received an inheritance of $70,000. She invested part at 10% and deposited the remainder in tax-free bonds at 8%. Her total annual income from the investments was $6200. Find the amount invested at 10%.

Solve the problem. -In a chemistry class, 9 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?