if owen has a collection of nickels and quarters worth $8.10. if the nickles were quarters and the quarters were nickels, the value would be 17.70 find the number of each coin?
Accepted Solution
A:
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=8.10Multiplying both sides by 20n+5q=162 (1)if the nickles were quarters and the quarters were nickels, the value would be $17.70i.e. 0.05q+0.25n=17.70Multiplying both sides by 20q+5n=354 (2)equation (1)×5-(2), we get5n+25q-(q+5n)=810-35424q=456dividing both sides by 24,we getq=19Putting q=19 in (2),we get19+5n=354Subtract both sides by 19,we get5n=335Dividing both sides by 5, we getn=67Hence, Number of nickle=67Number of quarter=19