Question

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i have 25 coins. some of them are dimes, and some of them are
quarters. in total, i have $5.20. how many dimes and how many
quarters do i have?

Answer 1

Answer:

• 18 quarters
• 7 dimes

Step-by-step explanation:

The given relations can be used to write two equations describing the coins. One equation can express the total number of coins; the other, their total value.

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setup

Let d and q represent the numbers of dimes and quarters, respectively. The the total number of coins is ...

  d + q = 25

and their total value is ...

  0.10d +0.25q = 5.20

solution

Using the first equation to write an expression for d, we can substitute that into the second equation.

  d = 25 -q

  0.10(25 -q) +0.25q = 5.20

  0.15q = 2.70 . . . . . . . . . collect terms, subtract 2.50

  q = 18 . . . . . . . . . . . divide by 0.15

  d = 25 -q = 7

You have 18 quarters and 7 dimes.

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Additional comment

It is generally convenient to solve for the number of the higher-value coin. That way, the numbers in the equations stay positive, tending to reduce errors.