anatoliy has a combination of 104 nickels and quarters totaling $22. which system of linear equations can be used to find the nu

Question

3 months ago

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anatoliy has a combination of 104 nickels and quarters totaling $22. which system of linear equations can be used to find the nu

mber of nickels, n, and the number of quarters, q, anatoliy has? n = q = 22 0.05n 0.25q = 104 n q = 104 5n 25q = 22 n q = 104 0.05n 0.25q = 22 n q = 22 5n 25q = 104

Mathematics

2 answers:

AnnZ [12.3K] · Answer 1 · 2026-02-22T17:46:14+03:00

Answer: The correct answer is the third option.

Detailed explanation:

It is stated that

The combined total of nickels and quarters is 104

The overall total value is $22

Define the number of nickels as n

Define the quarters as q

Consequently, the first equation will be

$n+q=104$

We know that

nickels are valued at 0.05 dollars

quarters at 0.25 dollars

Thus, the second equation will be

$0.05n+0.25q=\$22$

As a result, two systems of linear equations can assist in determining the number of nickels and quarters.

i.e.

$n+q=104\\\\0.05n+0.25q=\$22$

By using the elimination method, we can solve for n and q:

$n+q=104\\\\0.05n+0.25q=22$

0.05(n+q =104 )

⇒0.05n+0.05q=5.2-----------(3)

Now, using equations (2) and (3), we can deduce,

0.05n+0.05q=5.2

0.05n+0.25q=22

(-) (-) (-)

------------------------------------

0 +0.2q= 16.8

$q=\frac{16.8}{0.2}\\\\q=84\\\\n+q=104\\\\n+84=104\\\\n=104-84\\\\n=20$

Thus, the third option is the correct one.

babunello [11.8K] · Answer 2 · 2026-02-22T17:49:18+03:00

babunello [11.8K]3 months ago

4 0

Let n represent the number of nickels and q represent the quantity of quarters. Therefore,
n + q = 104
0.05n + 0.25q = 22