Answer: 25 quarters and 13 dimes
Step 1: Setup Coin Value and Coin Total Equation:
Coin Value Equation → 0.1d + 0.25q = $7.55 where d = dimes and q = quarters
Coin Total Equation → d + q = 38
Step 2: Rearrange Coin Total Equation in terms of dimes (d)
d = 38 - q ← Revised Coin Total Equation
Step 3: Plug in our Revised Coin Total Equation for d into our Coin Value Equation:
0.1(38 - q) + 0.25q = $7.55
0.1(38) - 0.1(q) + 0.25q = $7.55
3.8 - 0.1q + 0.25q = $7.55
3.8 + (0.25 - 0.1)q = $7.55
3.8 + 0.15q = $7.55
Step 4: Subtract 3.8 from each side of the equation to isolate q
3.8 - 3.8 + 0.15q = $7.55 - 3.8
0.15q = 3.75
Step 5: Divide each side of the equation by 0.15 to isolate q
0.15q/0.15 = 3.75 /0.15
q = 25
Step 6: Using our value for q, Solve for d using our Coin Total Equation:
d + 25 = 38
Subtracting 25 from both sides, we get d + 25 - 25 = 38 - 25
d = 13
Summarizing our word problem, we see that 25 quarters and 13 dimes add up to $7.55
