Question

zoe has a total of 16 coins. some of her coins are dimes and some are nickels. The combined value of her nickels and dimes is 1.35. How many nickels and dimes does she have?

Answer 1

Given:

In 16 coins some coins are dimes and some are nickels.

The combined value of her nickels and dimes is 1.35.

To find:

The number of nickels and dimes.

Solution:

We have,

Number of total coins = 16

Combined value = $1.35

Let x be the number of nickels and y be the number of dimes.

Total coins:
`x+y=16` ...(i)

We know that,

1 nickel = $0.05

1 dime = $0.10

Combined value:
`0.05x+0.10y=1.35` ...(ii)

From (i), we get

`y=16-x` ...(iii)

Putting this in (ii), we get

`0.05x+0.10(16-x)=1.35`

`0.05x+1.60-0.10x=1.35`

`-0.05x=1.35-1.60`

`-0.05x=-0.25`

Divide both sides by -0.05.

`x=(-0.25)/(-0.05)`

`x=5`

Putting x=5 in (ii), we get

`y=16-5`

`y=11`

Therefore, the number of nickels is 5 and the number of dimes is 11.