Respuesta :
Answer:
The drawer contains 40 nickels, 20 dimes and 14 quarters.
Step-by-step explanation:
Let d, q and n represent number of dimes, quarters and nickels respectively.
We have been given that there are twice as many nickels as dimes.
[tex]n=2d...(1)[/tex]
Further, the number of dimes and quarters sum to 34.
[tex]d+q=34...(2)[/tex]
As the change drawer contains $7.50 made up entirely of quarters, nickels, and dimes.
[tex]0.10d+0.25q+0.05n=7.50...(3)[/tex]
From equation (2), we will get:
[tex]q=34-d[/tex]
Substituting equation (1) and equation (2) in equation (3), we will get:
[tex]0.10d+0.25(34-d)+0.05(2d)=7.50[/tex]
[tex]0.10d+8.50-0.25d+0.10d=7.50[/tex]
[tex]-0.05d+8.50=7.50[/tex]
[tex]-0.05d+8.50-8.50=7.50-8.50[/tex]
[tex]-0.05d=-1[/tex]
[tex]\frac{-0.05d}{-0.05}=\frac{-1}{-0.05}[/tex]
[tex]d=20[/tex]
Therefore, drawer contains 20 dimes.
Substitute [tex]d=20[/tex] in equation (1):
[tex]n=2d[/tex]
[tex]n=2(20)[/tex]
[tex]n=40[/tex]
Therefore, drawer contains 40 nickels.
Substitute [tex]d=20[/tex] in equation (2):
[tex]20+q=34[/tex]
[tex]20-20+q=34-20[/tex]
[tex]q=14[/tex]
Therefore, drawer contains 14 quarters.
Answer:
There are 40 nickels, 14 quarters and 20 dimes.
Step-by-step explanation:
A change drawer contains $7.50
Let the number of quarters in the drawer = q
let the number of nickels in the drawer = n
and number of dimes = d
So, (0.25q + 0.05n + 0.10d) = 7.5
By dividing the equation by 0.50
5q + n + 2d = 150 ---------(1)
Now statement says " There are twice as nickels as dimes"
n = 2d -------(2)
And "the number of dimes and quarters sum to 34"
d + q = 34 -------(3)
We replace n = 2d from equation (2) in equation (1)
5q + 2d + 2d = 150
5q + 4d = 150 ---------(4)
Multiply equation (3) by 4 and subtract it from equation (4)
(5q + 4d) - 4(d + q) = 150 - 34×4
5q - 4q + 4d - 4d = 150 - 136
q = 14
We plug in the value of q in equation (3)
d + 14 = 34
d = 34 - 14
d = 20
Since n = 2d
So n = 2×20
n = 40
Therefore, there are 40 nickels, 14 quarters and 20 dimes.
