Landau has some nickels, dimes, amd quarters. the number of dimes is 3 more than 7 times the number of nickels. the number of quarters is 4 less than 2 times the number of nickels. the total value of the coin is 330 cents. write and solve an equation of each type of the coin

This question is one where the numbers don't add up. You should ask your teacher to show you how to work it.

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Let n, d, q represent the numbers of nickels, dimes, and quarters Landau has, respectively.

... d = 7n +3 . . . . . the number of dimes is 3 more than 7 times the number of nickels

... q = 2n -4 . . . . . the number of quarters is 4 less than 2 times the number of nickels

... 5n +10d +25q = 330 . . . . the total value of the coins is 330 cents

Using the first two equations to substitute into the last one, we get

... 5n +10(7n +3) +25(2n -4) = 330

... 125n -70 = 330 . . . . . . eliminate parentheses, collect terms

... n = 400/125 . . . . . . . . add 70, divide by 125

... n = 3.2

... d = 7·3.2 +3 = 25.4

... q = 2·3.2 -4 = 2.4

Landau has 3.2 nickels, 25.4 dimes, and 2.4 quarters.

answer is 144

step-by-step explanation: