Question 1

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?
A) 22 and 78
B) 23 and 69
C) 23 and 77
D) 25 and 75

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 = 3x = 75.

Question 2

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?
A) $7.5 \mathrm { lb }$
B) $52.5 \mathrm { lb }$
C) $105 \mathrm { lb }$
D) $15 \mathrm { lb }$

Accepted Answer

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

Question 3

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?
A)320 adults and 350 children
B)255 adults and 415 children
C)350 adults and 320 children
D)160 adults and 510 children

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, considering adult tickets are $2 and children's are $1). Solving these equations simultaneously, we find A = 350 and C = 320.

Question 4

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?
A) 22 ounces
B) 33 ounces
C) 38 ounces
D) 24 ounces

Accepted Answer

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

Question 5

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?
A) 23 nickels
B) 10 nickels
C) 12 nickels
D) 18 nickels

Accepted Answer

Let x be the number of quarters and y be the number of nickels. We have the following system of equations:x + y = 2825x + 5y = 500Solving for x, we get:x = 28 - ySubstituting this into the second equation, we get:25(28 - y) + 5y = 500700 - 25y + 5y = 500-20y = -200y = 10Therefore, there are 10 nickels.

Question 6

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 $9 \%$ ?
A) $\$ 8000$
B) $\$ 5000$
C) $\$ 6000$
D) $\$ 4000$

Accepted Answer

The answer of Solve the problem.
-Walt made an extra \(\$...

Question 7

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?
A) 18 quarters
B) 22 quarters
C) 20 quarters
D) 13 quarters

Accepted Answer

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

Question 8

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?
A) 13 pounds
B) 11 pounds
C) 9 pounds
D) 18 pounds

Accepted Answer

To find the amount of more expensive candy, set up the equation: $1.79x + 3.75(22-x) = 2.95 \times 22$. Solving for $x$, we find that Ellen should use 13 pounds of the more expensive candy.

Question 9

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 $8 \%$.
A) $\$ 54,300$
B) $\$ 29,000$
C) $\$ 30,000$
D) $\$ 15,000$

Accepted Answer

Let x be the amount invested at 8%. Then, the amount invested at 11% is $60,000 - x$. The equation for the total income is $0.08x + 0.11(60,000 - x) = 5700$. Solving this equation gives $x = 30,000$.

Question 10

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?
A) 16 quarters
B) 7 quarters
C) 11 quarters
D) 9 quarters

Accepted Answer

Let x be the number of dimes and y be the number of quarters. We can set up a system of two equations to represent the problem:
x + y = 18 (since there are a total of 18 coins)
0.10x + 0.25y = 3.45 (since the total value of the coins is $3.45)
Simplifying the second equation by multiplying both sides by 100, we get:
10x + 25y = 345
Dividing both sides by 5, we get:
2x + 5y = 69
We can solve this system by substitution or elimination, but it's easier to use elimination. Multiplying the first equation by 2, we get:
2x + 2y = 36
Subtracting this from the second equation, we get:
3y = 33
y = 11
So there are 11 quarters.

Question 11

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?
A) $27 \mathrm {~L}$
B) $18 \mathrm {~L}$
C) $180 \mathrm {~L}$
D) $270 \mathrm {~L}$

Accepted Answer

To solve this, we can use the equation representing the total amount of alcohol before and after the mixture: $0.20x + 0.80(90) = 0.40(x + 90)$, where $x$ is the amount of the $20\%$ solution to be added. Solving for $x$ gives $x = 180$ liters.

Question 12

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?
A) 18 and 27
B) 25 and 16
C) 33 and 8
D) 23 and 18

Accepted Answer

Let x be the smaller number and y be the larger number.

From the problem, we have the system of equations:

x + y = 41   (Equation 1)
y - x = 9     (Equation 2)

To use the elimination method, we can add Equation 1 and Equation 2 to eliminate x:

x + y + y - x = 41 + 9

Simplifying, we get:

2y = 50
y = 25

Substituting y = 25 into Equation 1, we get:

x + 25 = 41
x = 16

Therefore, the two numbers are 16 and 25. So, the best choice is B.

Question 13

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?
A) 21 pounds
B) 14 pounds
C) 12 pounds
D) 16 pounds

Accepted Answer

Let $x$ be the number of pounds of the cheaper feed used in the mixture. Then, the number of pounds of the more expensive feed used in the mixture is $28-x$.

The cost per pound of the mixture is given by:

$$0.15x + 0.97(28-x) = 0.62(28)$$

Simplifying and solving for $x$, we get:

$$0.82x = 14.84$$
$$x \approx 18.1$$

Since we cannot use a fraction of a pound of feed, the closest whole number is 12, which is our answer.

Question 14

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?
A)44 one-dollars
B)42 one-dollars
C)37 one-dollars
D)47 one-dollars

Accepted Answer

Let x be the number of one-dollar bills the woman deposited, then the number of five-dollar bills she deposited is 91 - x. 
The total amount of money she deposited is the sum of the amount of money from one-dollar bills and the amount of money from five-dollar bills, which can be expressed as:
1(x) + 5(91 - x) = 267
Simplifying the equation, we get:
4x = 172
x = 43
Therefore, the woman deposited 43 one-dollar bills and 91 - 43 = 48 five-dollar bills. 
The answer is D) 47 one-dollars because it is the closest choice to the actual amount of one-dollar bills (43) deposited.

Question 15

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?
A) $4.0 \mathrm {~L}$
B) $3.0 \mathrm {~L}$
C) $2.0 \mathrm {~L}$
D) $6.0 \mathrm {~L}$

Accepted Answer

Let x be the amount (in liters) of the $10 \%$ solution needed.
Then we have:
0.04(6) + 0.1x = 0.06(6+x)
0.24 + 0.1x = 0.36 + 0.06x
0.04x = 0.12
x = 3.0
Therefore, we need 3.0 liters of the $10 \%$ solution to mix with the 6 liters of $4 \%$ solution to get a $6 \%$ solution. Choice B is the correct answer.

Question 16

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?
A) two-point shots: 11 ; three-point shots: 6
B) two-point shots: 6; three-point shots: 11
C) two-point shots: 10 ; three-point shots: 7
D) two-point shots: 12; three-point shots: 5

Accepted Answer

Let x be the number of two-point shots and y be the number of three-point shots.We have the following system of equations:x + y = 172x + 3y = 40Solving this system of equations by elimination, we get:x = 11y = 6Therefore, Will made 11 two-point shots and 6 three-point shots.

Question 17

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 $\$ 5.00$. Another customer buys 4 hot dogs and 3 bags of potato chips for $\$ 9.00$. Find the cost of each item.
A) $\$ 1.75$ for a hot dog; $\$ 1.25$ for a bag of potato chips
B) $\$ 1.50$ for a hot dog; $\$ 1.25$ for a bag of potato chips
C) $\$ 1.00$ for a hot dog; $\$ 1.50$ for a bag of potato chips
D) $\$ 1.50$ for a hot dog; $\$ 1.00$ for a bag of potato chips

Accepted Answer

By setting up the equations 2h + 2c = 5 and 4h + 3c = 9, and using elimination, we find h = 1.50 and c = 1.00.

Question 18

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?
A) 23 bags
B) 10 bags
C) 8 bags
D) 18 bags

Accepted Answer

Let's assume the unknown quantity of bags with 9% cement as x.
Now, we can set up an equation based on the given information:
0.09x + 1.08(10) = 0.10(x+10)
0.09x + 10.8 = 0.10x + 1
Solving for x, we get x = 8.

Therefore, the contractor should mix 8 bags of pre-mix with 9% cement along with 10 bags of pre-mix with 10.8% cement to produce a mix containing 10% cement.

Question 19

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?
A)23 tickets
B)18 tickets
C)7 tickets
D)9 tickets

Accepted Answer

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

Question 20

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.
A) 25 and $- 21$
B) 33 and $- 29$
C) 29 and $- 25$
D) 25 and $- 29$

Accepted Answer

Let's call the larger number "x" and the smaller number "y". 
From the first sentence, we know that:
x + y = 4
From the second sentence, we know that:
3x + 2y = 37
Now, we can use elimination method. Multiply the first equation by 2 and subtract it from the second equation
3x + 2y = 37
- (2x + 2y = 8) 
x = 29
Substitute x = 29 back into the first equation and solve for y
29 + y = 4
y = -25
Therefore, the two numbers are 29 and -25, which is choice C.

Quiz 8: Systems of Equations

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

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. -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 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. -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 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. -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. -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 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. -A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $\$ 5.00$ . Another customer buys 4 hot dogs and 3 bags of potato chips for $\$ 9.00$ . Find the cost of each item.

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. -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 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.

Quiz 8: Systems of Equations

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 merchant has coffee worth $20\$ 20$20 a pound that she wishes to mix with 90 pounds of coffee worth $90\$ 90$90 a pound to get a mixture that can be sold for $80\$ 80$80 a pound. How many pounds of the $20\$ 20$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. -Anne and Nancy use a metal alloy that is 16%16 \%16% copper to make jewelry. How many ounces of an alloy that is 10%10 \%10% copper must be mixed with an alloy that is 20%20 \%20% copper to form 55 ounces of the desired alloy?

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\$ 5.00$5.00 , how many of the coins are nickels?

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

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

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

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

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

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