Question

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?

Answer 1

We can model this situation as a system of linear equation, where n is the number of nickels and q is the number of quarters.

$\left \{ {{0.05n + 0.25q=8.10} \atop {0.25n+0.05q=17.70}} \right.$

Solving the system of equations,  there are 67 nickels and 19 quarters.

Answer 2

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