Question

HELP. there are 45 coins consisting of nickels, dimes and quarter making a total of 7 dollars. the number of dimes exceeds the number of nickels by five how many quarters are there

Answer 1

9514 1404 393

Answer:

  20

Step-by-step explanation:

Let n, d, q represent the numbers of nickels, dimes, and quarters, respectively. Then we have ...

  n + d + q = 45

  5n +10d +25q = 700

  n -d = -5

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Using n=d -5, we can substitute into the first two equations:

  (d -5) +d + q = 45

  2d +q = 50 . . . . add 5, collect terms [eq4]

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  5(d -5) +10d +25q = 700

  15d +25q = 725 . . . . . . . . . . add 25, collect terms [eq5]

Multiplying [eq4] equation by 3 and subtracting that from 2/5 of [eq5], we have ...

  (2/5)(15d +25q) -3(2d +q) = (2/5)(725) -3(50)

  6d +10q -6d -3q = 290 -150

  7q = 140 . . . . . . simplify

  q = 20 . . . . . . . . divide by 7

There are 20 quarters.