Answer: Third option is correct.
Step-by-step 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
[tex]n+q=104[/tex]
Since we know that
value of nickels = 0.05 dollars
Value of quarters = 0.25 dollars
Second equation will be
[tex]0.05n+0.25q=\$22[/tex]
So, there are two system of linear equation can be used to find the number of nickels and the number of quarters.
i.e.
[tex]n+q=104\\\\0.05n+0.25q=\$22[/tex]
Using elimination we can find the value of n and q :
[tex]n+q=104\\\\0.05n+0.25q=22[/tex]
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
[tex]q=\frac{16.8}{0.2}\\\\q=84\\\\n+q=104\\\\n+84=104\\\\n=104-84\\\\n=20[/tex]
Hence, third option is correct.
