A piggy bank contains 36 coins that consists of dimes and quarters totaling $5.85. How many quarters are in the piggy bank? In your final answer, include all necessary calculations.
Let's use algebra to solve the problem.
Let d be the number of dimes in the piggy bank.
Let q be the number of quarters in the piggy bank.
We know that:
d + q = 36 (because there are 36 coins in total)
0.1d + 0.25q = 5.85 (because the value of all the coins is $5.85)
We want to solve for q. Let's rearrange the first equation to get:
d = 36 - q
Now we can substitute this into the second equation:
0.1(36-q) + 0.25q = 5.85
Expand and simplify:
3.6 - 0.1q + 0.25q = 5.85
0.15q = 2.25
q = 15
So there are 15 quarters in the piggy bank. To check, we can substitute q = 15 into either equation and solve for d:
d + 15 = 36
d = 21
Now we can check that the total value of all the coins is $5.85:
0.1(21) + 0.25(15) = 5.85
2.1 + 3.75 = 5.85
5.85 = 5.85
It checks out!