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Jon has quarters, dimes, and nickels in his pocket. The value of his money is $1.75. There are two more dimes than quarters and twice as many nickels as dimes. How many nickels does he have? [?] nickels

Jon has quarters, dimes, and nickels in his pocket. The value of his money is $1.75. There-example-1
User ElMarquis
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1 Answer

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In order to determine the number of nickels Jon has, it is ncessary to write the given situation in an algebraic way.

If x is the number of quarters, y the number of dimes and z the number of nickels, then, 0.25x + 0.1y + 0.05z is the total amount of money Jon has.

The value of the money john has is $1.75, then you have:

0.25x + 0.1y + 0.05z = 1.75 (1)

There are two more dimes than quarters:

y = x + 2

z = 2y = 2(x + 2) = 2x + 4

replace the previous expressions for y and z into the equation (1) and solve for x:

0.25x + 0.1y + 0.05z = 1.75

0.25x + 0.1(x + 2) + 0.05(2x + 4) = 1.75 apply distribution property

0.25x + 0.1x + 0.1(2) + 0.05(2x) + 0.05(4) = 1.75

0.25x + 0.1x + 0.2 + 0.1x + 0.2 = 1.75 order like terms

0.25x + 0.1x + 0.1x + 0.2 + 0.2 = 1.75 simplify like terms left side

0.45x + 0.4 = 1.75 subtract 0.4 both sides

0.45x = 1.75 - 0.4

0.45x = 1.35 divide by 0.45 both sides

x = 1.35/0.45

x = 3

To determine the number of nickels, replace x into the expression for z:

z = 2x + 4

z = 2(3) + 4

z = 6 + 4

z = 10

Hence, Joh has 10 nickels

User Thomas Flinkow
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