Question

Lynn has $8.58 in quarters and pennies. If she has eight times ans many pennies as quarters, how many of each does she have?

Answer 1

Let q = number of quarters.
Let p = number of pennies.

A quarter is worth $0.25. q quarters are worth 0.25q.
A penny is worth $0.01. p pennies are worth 0.01p.
All coins together are worth 0.25q + 0.01p.

We are told that all coins together are worth $8.58, so 0.25q + 0.01p must equal 8.58.

0.25q + 0.01p = 8.58

That is our first equation.

She has 8 times as many pennies as quarters, so

p = 8q

That is our second equation.

We have a system of equations.

0.25q + 0,.01p = 8.58
p = 8q

Since the second equation is already solved for p, we can use the substitution method.

We will substitute 8q for p in the first equation.

0.25q + 0.01p = 8.58

0.25q + 0.01(8q) = 8.58

0.25q + 0.08q = 8.58

0.33q = 8.58

q = 26

p = 8q = 8 * 26 = 208

She has 26 quarters and 208 pennies.

Check:
26 quarters are worth 26 * $0.25 = $6.50
208 pennies are worth $2.08
$6.58 + $2.08 = $8.58
The value of the coi8ns is correct.

Also, 208/26 = 8. The number of pennies is really 8 times the number of quarters.

Our solution is correct.