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
Owen had a collection of 67 nickels and 19 quarters.
Let x represent the number of nickels and y represent the number of quarters.
A nickel is worth 5 cents ($0.05) while a quarter is worth 25 cents ($0.25).
Since Owen collection of nickels and quarters worth $8.10, hence:
0.05x + 0.25y = 8.10 (1)
If the nickles were quarters and the quarters were nickels, the value would be 17.70, hence:
0.25x + 0.05y = 17.70 (2)
Solving equation 1 and 2 simultaneously gives:
x = 67, y = 19
Hence Owen had a collection of 67 nickels and 19 quarters.
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