Answer with Step-by-step explanation:
Let there be n nickle and q quarters
Owen has a collection of nickels and quarters worth $8.10.
i.e. 0.05n+0.25q=8.10
Multiplying both sides by 20
n+5q=162 (1)
if the nickles were quarters and the quarters were nickels, the value would be $17.70
i.e. 0.05q+0.25n=17.70
Multiplying both sides by 20
q+5n=354 (2)
equation (1)×5-(2), we get
5n+25q-(q+5n)=810-354
24q=456
dividing both sides by 24,we get
q=19
Putting q=19 in (2),we get
19+5n=354
Subtract both sides by 19,we get
5n=335
Dividing both sides by 5, we get
n=67
Hence, Number of nickle=67
Number of quarter=19