Question

Anthony has a combination of 104 nickels and quarters totaling $22. Which system of linear equations can be used to find the number of nickels, and the number of quarters, , Anthony has?\

Answer 1

Anthony has 20 nickels and 84 quarters

Explanation:

Each nickel is worth $0.05, while each quarter is worth $0.25, therefore the number of nickels and quarters multiplied by their respective values must be equal to the total of money Anthony has:

0.05*nickel + 0.25*quarter = 22

And the sum of the number of nickels and quarters must be equal to the total number of coins he has:

nickel + quarter = 104

So the system is:

0.05*nickel + 0.25*quarter = 22

nickel + quarter = 104

To solve this we will multiply the second equation by -0.25

0.05*nickel + 0.25*quarter = 22

-0.25*nickel -0.25*quarter = -26

We now sum the equations:

-0.20*nickel = -4

nickel = -4/(-0.2) = 20

Using the second equation we can find the number of quarters:

20 + quarter = 104

quarter = 104 - 20 = 84

Answer 2

x + y = 104

0.05x + 0.25y = 22

x = 20 niquels and y = 84 quarters

Explanation:

Each niquel is $0.05, and each quarter is $0.25

So if we have x niquels and y quarters, we can set this system of equations:

x + y = 104 (eq1)

0.05x + 0.25y = 22 (eq2)

If we multiply the second equation by 4, and then subtract it from the first equation, we have:

(eq2)*4: 0.2x + y = 88

(eq1) - 4*(eq2): 0.8x = 16

x = 20

Now finding y with the first equation:

20 + y = 104

y = 84