Brian has saved five dollars in dimes quarters and half dollars she finds that she has 30 coins all together and there are four times as many quarters as there are half dollars how many dimes does Brian have

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Step-by-step explanation:

Let d, q, h represent the numbers of dimes, quarters, and halves Brian has. We can write 3 equations in these 3 variables:

  10d +25q +50h = 500 . . . . value of the coins, in cents

  d + q + h = 30 . . . . . . . . . . . total number of coins

  4h = q . . . . . . . . . . . . . . . . . four times as many quarters as halves

Using the last equation to substitute into the other two, we get ...

  10d + 150h = 500

  d +5h = 30

The second equation can be written as ...

  5h = 30 -d

and the first can be written to facilitate substitution:

  10d +30(5h) = 500

  10d +30(30-d) = 500 . . . . . substitute for 5h

  900 -20d = 500 . . . . . . . . . simplify

  400 = 20d . . . . . . . . . . . . . add 20d-500 to both sides

  d = 20 . . . . . . . . . . . . . . . . divide by 20

Brian has 20 dimes.