Question

now answer the question:
harper has $0.70 worth of nickels and dimes. she has 5 more nickels than dimes. determine the number of nickels, x, and the number of dimes, y, that harper has.
answer
harper has
\tnickels and
\tdimes.

Explanation:

Step1: Define variables and equations

Let \( x \) be the number of nickels and \( y \) be the number of dimes. We know two things:

1. The value of the coins: A nickel is $0.05 and a dime is $0.10, so \( 0.05x + 0.10y = 0.70 \).
2. The number of nickels is 5 more than dimes: \( x = y + 5 \).

Step2: Substitute \( x \) into the value equation

Substitute \( x = y + 5 \) into \( 0.05x + 0.10y = 0.70 \):
\( 0.05(y + 5) + 0.10y = 0.70 \)

Step3: Expand and simplify

Expand the left side: \( 0.05y + 0.25 + 0.10y = 0.70 \)
Combine like terms: \( 0.15y + 0.25 = 0.70 \)

Step4: Solve for \( y \)

Subtract 0.25 from both sides: \( 0.15y = 0.70 - 0.25 = 0.45 \)
Divide both sides by 0.15: \( y = \frac{0.45}{0.15} = 3 \)

Step5: Solve for \( x \)

Use \( x = y + 5 \), so \( x = 3 + 5 = 8 \)

Answer:

Harper has 8 nickels and 3 dimes.