Let:
p = number of pennies (one cent)
q = number of quarters (25 cents)
d = number of dimes (10 cents)
The total number of coins in the box is 75, thus:
p + q + d = 75
This gives us the first equation.
We also know there are 4 times as many pennies as quarters, thus:
q = 4p
We also know there are 3 more dimes than quarters, thus:
d = q + 3
Since q = 4p:
d = 4p + 3
It's required to find the number of pennies in the box (p).
Substituting the last two equations in the first one:
p + 4p + 4p + 3 = 75
Simplifying:
9p = 72
Dividing by 9:
p = 8
There are 8 pennies in the box
To complete the answer, we find:
q = 4*8 = 32
d = 32 + 3 = 35
There are also 32 quarters and 35 dimes in the box
