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.
