Question

Elina is gathering up change she has saved. She has a total of $2.60. All of her change is in either nickles, dimes, or quarters. She has twice as many dimes as quarters and two less quarters than nickles. If the number of quarters Elina has is represents by the variable n, write an equation that models this problem and solve it for the number of each type of coin. (I keep getting 1.15 but it doesn't make sense if n=1.15 when n is how many quarters there are so please help.)

Answer 1

Given

Elina is gathering up change she has saved

She has a total of $2.60.

All of her change is in either nickles, dimes, or quarters.

She has twice as many dimes as quarters and two less quarters than nickles.

Find out how many quaters Elina have.

To proof

As given

number of quarters Elina has is represents by the variable = n

She has twice as many dimes as quarters

Number of dimes = 2n

two less quarters than nickles.

Number of nickels = n + 2

1nickel = $0.05 ,

1quaters = $ 0.25

1dimes = $0.10

Than the equation become in the form

0.25n + 0.10× 2n + 0.05× ( n + 2) = 2.60

0.25n + 0.20n + 0.05n + 0.1 = 2.60

0.5n = 2.5

`n = (2.5)/(0.5)`

n = 5

Number of quaters = 5

Number of dimes = 2× 5

= 10

Number of nickel = 5+ 2

= 7

Therefore the number of quaters are 5.

Hence proved

Answer 2

Let the number of nickels be = x

Let the number of dimes be = d

Let the number of quarter be = n

Given is, she has twice as many dimes as quarters

d=2n or n = 0.5d

She has two less quarters than nickles.

n= x-2 or

x= n+2

Total values of coins is = $2.60

`0.05x+0.10d+0.25n=2.60`

Now replace x with (n+2) and d with 2n

`0.05(n+2)+0.10(2n)+0.25n=2.60`

`0.05n+0.10+0.20n+0.25n=2.60`

`0.50n+0.10=2.60`

`0.50n=2.50`

`n=5`

Now x=n+2 ; x=5+2 = 7

d=2n ; d=2(5) = 10

Hence, Elina has 7 nickels, 10 dimes and 5 quarters.