Question

Jonathon has a collection of coins worth a total of $10.75. If he has one-fourth as many dimes as pennies, and two-thirds as many dimes as nickels, how many of each coin does Jonathon have?

Answer 1

10.35 collections for the coin s worth

Answer 2

The number of dimes, pennies and nickels are required.

The number of dimes is 50, pennies is 200 and nickels is 75.

Let the number of dimes be $x$

From the question the number of dimes is one-fourth the number of pennies and two-thirds the number of nickels.

So,

The number of pennies is $4x$

and number of nickels is $\dfrac{3}{2}x$

1 nickel = 0.05$

1 penny = 0.01$

1 dime = 0.01$

Total value of the coins is $10.75

$0.1x+0.05\times \dfrac{3}{2}x+0.01\times 4x=10.75\\\Rightarrow 0.215x=10.75\\\Rightarrow x=\dfrac{10.75}{0.215}\\\Rightarrow x=50$

The number of dimes is 50.

The number of pennies is $4x=4\times50=200$

The number of nickels is $\dfrac{3}{2}x=\dfrac{3}{2}\times50=75$.

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