Respuesta :
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
[tex]n = \frac{2.5}{0.5}[/tex]
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
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
[tex]0.05x+0.10d+0.25n=2.60[/tex]
Now replace x with (n+2) and d with 2n
[tex]0.05(n+2)+0.10(2n)+0.25n=2.60[/tex]
[tex]0.05n+0.10+0.20n+0.25n=2.60[/tex]
[tex]0.50n+0.10=2.60[/tex]
[tex]0.50n=2.50[/tex]
[tex]n=5[/tex]
Now x=n+2 ; x=5+2 = 7
d=2n ; d=2(5) = 10
Hence, Elina has 7 nickels, 10 dimes and 5 quarters.
