Question

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

Answer 1

Answer: Third option is correct.

Explanation:

Since we have given that

Number of nickels and quarters = 104

Total amount from them = $22

Let the number of nickels be n

Let the quarters be q

So, First equation will be

`n+q=104`

Since we know that

value of nickels = 0.05 dollars

Value of quarters = 0.25 dollars

Second equation will be

`0.05n+0.25q=\$22`

So, there are two system of linear equation can be used to find the number of nickels and the number of quarters.

i.e.

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

Using elimination we can find the value of n and q :

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

0.05(n+q =104 )

⇒0.05n+0.05q=5.2-----------(3)

Now, from equation (2) and (3), we get,

0.05n+0.05q=5.2

0.05n+0.25q=22

(-) (-) (-)

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

0 +0.2q= 16.8

`q=(16.8)/(0.2)\\\\q=84\\\\n+q=104\\\\n+84=104\\\\n=104-84\\\\n=20`

Hence, third option is correct.

Answer 2

Let the number of nickels be n and that of quarters be q. Then
n + q = 104
0.05n + 0.25q = 22