Question

A scuba diver, hired by an amusement park, collected $142 in nickels, dimes, and quarters at the bottom of a wishing well. There were 500 nickels, and 90 more quarters than dimes. How many quarters and dimes were thrown into the wishing well?

Dimes?

Quarters?

Answer 1

We have total amount = $142

Value of total nickels = 500*0.05 = $25
So, amount of dimes & quarters = 142 – 25 = $117
Now we will subtract “extra” 90 quarters from this amount, this will give us equal numbers of quarters and dimes, so we have now:
$117 – (90 * 0.25 = $22.5) = $94.5
Now $94.5 has equal number of dimes (d) and quarters (q), so
d * 0.10 + q * 0.25 = $94.5
Since d = q, so 0.35*q = 94.5
or q = 9450/35 = 270
So, dimes = 270
quarters = 270+90 = 360
Verify :
270*0.10 = $27
360*0.25 = $90
500*0.05 = $25
Total = $142