Question

Anurak has nickels, dimes, and pennies in his pocket. The coins in Anurak's pocket have a total value of 75 cents. He has three more nickels than dimes and five times as many pennies as dimes. How many coins of each type does Anurak have?

Answer 1

Anurak has 15 pennies, 6 nickels and 3 dimes.

Explanation:

Answer 2

Anurak has 15 pennies, 6 nickels and 3 dimes.

Explanation:

We must have these informations in mind:

1) A penny is a 1-cent coin.

2) A dime is a 10-cent coin.

3) A nickel is a 5-cent coin.

Let be
`x`,
`y`,
`z` the quantities of pennies, nickels and dimes, respectively. From statement we get that to value in Anurak's pocket is represented by this mathematical expression:

`0.01\cdot x + 0.05 \cdot y + 0.10\cdot z = 0.75` (Eq. 1)

In addition, we get the following identities:

i) He has three more nickels than dimes

`z + 3 = y` (Eq. 2)

ii) And five times as many pennies as dimes

`x = 5\cdot z` (Eq. 3)

The system of linear equations is now reduced: (Eqs. 2, 3) in (Eq. 1)

`0.05\cdot z +0.05\cdot z + 0.15 + 0.10\cdot z = 0.75`

`0.20\cdot z = 0.60`

`z = 3`

The remaining variables are
`y = 6` and
`x = 15`.

Anurak has 15 pennies, 6 nickels and 3 dimes.