Question

Quiz
Question 1 (1 point)

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Aiden has a collection of 63 nickels and quarters in his piggy bank. If the total value of the coins is $10.75. How many nickels does he have? How many quarters does he have?

Question 1 options:

20 nickels and 43 quarters


25 nickels and 38 quarters


18 nickels and 45 quarters


38 nickels and 25 quarters

Question 2 (1 point)

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The sum of two numbers is 25. One number is twice the second number plus 7. What are the two numbers?

Question 2 options:

18 and 7


15 and 10


19 and 6


20 and 5

Question 3 (1 point)

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Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each coin does he have?

Question 3 options:

16 nickels and 33 quarters


32 nickels and 17 quarters


17 nickels and 32 quarters


25 nickels and 24 quarters

Question 4 (1 point)

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Max has a collection of 99 dimes and pennies worth $4.41. How many of each coin does he have.

Question 4 options:

40 dimes and 59 pennies


34 dimes and 65 pennies


61 dimes and 38 pennies


38 dimes and 61 pennies

Question 5 (1 point)

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The sum of the two numbers in 53. Their difference is 25. Find both numbers.

Question 5 options:

16 and 37


30 and 23


42 and 11


39 and 14


0 of 5 questions saved
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Answer 1

Let's solve each of the questions one by one.

### Question 1:
Aiden has a collection of 63 nickels and quarters and their total value is $10.75.

Let:
- \( n \) be the number of nickels
- \( q \) be the number of quarters

We have the following equations:

1. \( n + q = 63 \) (total number of coins)
2. \( 0.05n + 0.25q = 10.75 \) (total value of coins in dollars)

To simplify the second equation, we can multiply everything by 100 to eliminate decimals:

\[
5n + 25q = 1075
\]

Now we have the system of equations:

1. \( n + q = 63 \)
2. \( 5n + 25q = 1075 \)

From equation (1), we can express \( n \) as \( n = 63 - q \).

Substituting into equation (2):

\[
5(63 - q) + 25q = 1075
\]
\[
315 - 5q + 25q = 1075
\]
\[
20q = 1075 - 315
\]
\[
20q = 760
\]
\[
q = 38
\]

Substituting \( q \) back to find \( n \):

\[
n = 63 - 38 = 25
\]

So, Aiden has **25 nickels and 38 quarters**.

### Question 2:
The sum of two numbers is 25. One number is twice the second number plus 7.

Let:
- \( x \) be the first number
- \( y \) be the second number

We have the equations:

1. \( x + y = 25 \)
2. \( x = 2y + 7 \)

Substituting equation (2) into (1):

\[
2y + 7 + y = 25
\]
\[
3y + 7 = 25
\]
\[
3y = 18
\]
\[
y = 6
\]

Substituting \( y \) back into (1):

\[
x + 6 = 25
\]
\[
x = 19
\]

The two numbers are **19 and 6**.

### Question 3:
Dustin has 49 coins total for a combined value of $8.85.

Let:
- \( n \) be the number of nickels
- \( q \) be the number of quarters

We have the equations:

1. \( n + q = 49 \)
2. \( 0.05n + 0.25q = 8.85 \)

Multiplying the second equation by 100:

\[
5n + 25q = 885
\]

Substituting \( n = 49 - q \) into the second equation:

\[
5(49 - q) + 25q = 885
\]
\[
245 - 5q + 25q = 885
\]
\[
20q = 885 - 245
\]
\[
20q = 640
\]
\[
q = 32
\]

Now substituting \( q \) back to find \( n \):

\[
n = 49 - 32 = 17
\]

Dustin has **17 nickels and 32 quarters**.

### Question 4:
Max has 99 dimes and pennies worth $4.41.

Let:
- \( d \) be the number of dimes
- \( p \) be the number of pennies

We have:

1. \( d + p = 99 \)
2. \( 0.10d + 0.01p = 4.41 \)

Multiplying the second equation by 100:

\[
10d + p = 441
\]

Now substituting \( p = 99 - d \) into the second equation:

\[
10d + (99 - d) = 441
\]
\[
10d + 99 - d = 441
\]
\[
9d + 99 = 441
\]
\[
9d = 342
\]
\[
d = 38
\]

Substituting \( d \) back to find \( p \):

\[
p = 99 - 38 = 61
\]

Max has **38 dimes and 61 pennies**.

### Question 5:
The sum of the two numbers is 53. Their difference is 25.

Let the two numbers be \( x \) and \( y \).

We have:

1. \( x + y = 53 \)
2. \( x - y = 25 \)

Adding the two equations together:

\[
(x + y) + (x - y) = 53 + 25
\]
\[
2x = 78
\]
\[
x = 39
\]

Now substituting \( x \) back to find \( y \):

\[
39 + y = 53
\]
\[
y = 14
\]

The two numbers are **39 and 14**.

### Summary of Answers:
1. **25 nickels and 38 quarters**
2. **19 and 6**
3. **17 nickels and 32 quarters**
4. **38 dimes and 61 pennies**
5. **39 and 14**