Izzy is Iago's little sister. She is counting her coins. Izzy finds that she has three more quarters ($0.25) than she has dimes ($0.10), twice as many nickels ($0.05) as she has dimes, and four times as many pennies ($0.01) as she has dimes. With a total of $7.61 in coins, how many coins of each type does Izzy have?

Question

Mathematics

Lea Yoder

4 August, 04:07

Izzy is Iago's little sister. She is counting her coins. Izzy finds that she has three more quarters ($0.25) than she has dimes ($0.10), twice as many nickels ($0.05) as she has dimes, and four times as many pennies ($0.01) as she has dimes. With a total of $7.61 in coins, how many coins of each type does Izzy have?

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Araceli Jimenez · Answer 1

Lzzy has three more quarters ($0.25) than she has dimes ($0.10), twice as many nickels ($0.05) as she has dimes, and four times as many pennies ($0.01) as she has dimes.

Let us assume number of dimes = x.

"Three more quarters than dimes" would be = (x+3) quarters.

"Twice as many nickels as dimes " would be = (2x) nickels.

"Four times as many pennies as dimes" would be = (4x) pennies.

Total value of all coins = $7.61.

We can setup an equation now.

0.10*x + 0.25 (x+3) + 0.05 (2x) + 0.01 (4x) = 7.61.

Let us simplify the equation.

0.10x + 0.25x + 0.75 + 0.10x + 0.04x = 7.61

0.49x + 0.75 = 7.61.

Subtratcing 0.75 from both sides, we get

0.49x = 6.86

Dividing both sides by 0.49, we get

x = 14.

Therefore,

Number of dimes = x = 14. Number of quarters = (x+3) = 14+3 = 17. Number of nickels = 2x = 2*14 = 28. Number of pennies = 4x = 4*14 = 56.