Tia received $7.55 in change in quarters and dimes. There were 38 coins in all. How many of each kind did she

receive?

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

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step-by-step explanation:

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