Question

Betty has 741 coins in her piggy bank, worth a total of 10,725 cents. The piggy bank only contains quarters and dimes. How many dimes does Betty have?

Answer 1

Let quarters = q and
Dimes = d

We have 741 coins total so q + d = 741

Since quarters are 25 cents and Dimes are 10 cents then

25q + 10d = 10725 cents

Now we have 2 equations that we can solve using addition or substitution.

Using addition, first multiply the first equation by -10

-10 (q+d) = 741 (-10)
-10q - 10d = -7410

Now add the equations together

(-10q -10d = -7410)
+ (25q + 10d =10725)
________________
15q = 3315
q = 3315 / 15
q = 221
this is the number of quarters

Now plug this back into the original equation

q + d = 741
221 + d = 741
d = 741 - 221
d = 520

There are 520 dimes