Answer:
# of quarters: 76
# of dimes: 96
Explanation:
Thomas has 172 coins in the bucket. Let 'd' describe the number of dimes and let 'q' decide the number of quarters.
So, we can write: d+q=172
The total in the bucket is $28.60. The total amount of money in dimes is equal to the number of dimes multiplied by the value of one dime ($0.10), and the total amount of money in quarters is equal to the number of quarters multiplied by the value of one quarter ($0.25).
So, we can write: 0.1d+0.25q=28.6
We know d+q=172, which means q=172-.
Let's sub this into our second equation to get our answer:
0.1d+0.25q=28.6
0.1(172-q)+0.25q=28.6
17.2-0.1q+0.25q=28.6
0.15q=11.4
q=76
Now let's sub this value for q into our first equation:
d+q=172
d+76=172
d=96