You have 55 coins in your pocket
consisting of dimes and quarters with a total value of $8.50
How many dimes and quarters do you have?
Step 1: Setup Coin Value and Coin Total Equation:
Coin Value Equation
0.1d + 0.25q = $8.50
where d = dimes and q = quarters
Coin Total Equation → d + q = 55
Step 2: Rearrange Coin Total Equation in terms of dimes (d)
d = 55 - q ← Revised Coin Total Equation
Step 3: Plug in our Revised Coin Total Equation for d into our Coin Value Equation:
0.1(55 - q) + 0.25q = $8.50
0.1(55) - 0.1(q) + 0.25q = $8.50
5.5 - 0.1q + 0.25q = $8.50
5.5 + (0.25 - 0.1)q = $8.50
5.5 + 0.15q = $8.50
Step 4: Subtract 5.5 from each side of the equation to isolate q
5.5 - 5.5 + 0.15q = $8.50 - 5.5
0.15q = 3
Step 5: Divide each side of the equation by 0.15 to isolate q
| 0.15q | |
| 0.15 |
| = |
| 3 |
| 0.15 |
q = 20
Step 6: Using our value for q, Solve for d using our Coin Total Equation:
d + 20 = 55
Subtracting 20 from both sides, we get d + 20 - 20 = 55 - 20
d = 35
Final Answer
20 quarters and 35 dimes adds up to $8.50
