8 more dimes than quarters coins in with a total value of $22.00

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You have $22.00 worth of coins consisting of dimes and quarters

You have 8 more dimes than quarters

How many dimes and quarters do you have?

Step 1: Setup Coin Value and Coin Total Equation:

Coin Value Equation → 0.1d + 0.25q = $22.00 where d = dimes and q = quarters

Step 2: Rearrange Coin Total Equation in terms of dimes (d)

Since we have 8 more dimes than quarters, we set up our relational equation as follows:

Coin Total Equation → d = q + 8

d = q + 8  ← Revised Coin Total Equation

Step 3: Plug in our Revised Coin Total Equation for d into our Coin Value Equation:

0.1(q + 8) + 0.25q = $22.00

0.1(8) + 0.1(q) + 0.25q = $22.00

0.8 + 0.1q + 0.25q = $22.00

0.8 + (0.25 + 0.1)q = $22.00

0.8 + 0.35q = $22.00

Step 4: Subtract 0.8 from each side of the equation to isolate q

0.8 - 0.8 + 0.35q = $22.00 - 0.8

0.35q = 21.2

Step 5: Divide each side of the equation by 0.35 to isolate q

Cancel 0.35 on the left side:

q = 60.571428571429

Step 6: Solve for d using our Coin Total Equation:

d = q + 8

Substitute q = 60.571428571429

d = 60.571428571429 + 8

d = 68.571428571429

Final Answer