Question

Raekwon has a coin collection consisting of nickels and dimes. He has 28 coins worth $2.25. How many of each coin does Raekwon have?

Answer 1

There are 11 nickels and 17 dimes

Solution:

Let "d" be the number of dimes

Let "n" be the number of nickels

Remember that a dime is worth 10 cents and nickel is worth 5 cents

He has 28 coins worth $2.25

number of dimes + number of nickels = 28

d + n = 28 --------- eqn 1

The worth is $ 2.25. Therefore, we frame a equation as:

2.25 dollar is worth 225 cents

number of dimes x Value of 1 dime + number of nickels x Value of 1 nickel = 225

`d * 10 + n * 5 = 225\\\\10d + 5n = 225 ---------- eqn 2`

From eqn 1,

d = 28 - n -------- eqn 3

Substitute eqn 3 in eqn 2

10(28 - n) + 5n = 225

280 - 10n + 5n = 225

5n = 55

n = 11

Substitute n = 11 in eqn 3

d = 28 - 11

d = 17

Thus there are 11 nickels and 17 dimes