Question

michael has $1.65 worth of nickels and dimes. he has 6 more nickels than dimes. determine the number of nickels and the number of dimes that michael has.

answer attempt 1 out of 4

there are \boxed{} nickels and \boxed{} dimes.

Explanation:

Step1: Define variables for coins

Let $d$ = number of dimes, $n = d + 6$ (nickels = dimes +6)

Step2: Set up value equation

Each nickel = $0.05$, each dime = $0.10$. Total value:
$$0.05n + 0.10d = 1.65$$

Step3: Substitute $n$ into equation

Replace $n$ with $d+6$:
$$0.05(d+6) + 0.10d = 1.65$$

Step4: Expand and simplify

$$0.05d + 0.30 + 0.10d = 1.65$$
$$0.15d + 0.30 = 1.65$$

Step5: Solve for $d$

Subtract 0.30, divide by 0.15:
$$0.15d = 1.65 - 0.30 = 1.35$$
$$d = \frac{1.35}{0.15} = 9$$

Step6: Calculate number of nickels

Use $n = d + 6$:
$$n = 9 + 6 = 15$$

Answer:

There are 15 nickels and 9 dimes.