Question

Kevin and Randy Muise have a jar containing 62 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $10.90

Answer 1

Explanation:

q = number of quarters ($0.25 per coin)

n = number of nickels ($0.05 per coin)

q + n = 62

q×0.25 + n×0.05 = 10.9

from the first equation we get for example

q = 62 - n

and we use that in the second equation

(62 - n)×0.25 + n×0.05 = 10.9

15.5 - n×0.25 + n×0.05 = 10.9

15.5 - n×0.2 = 10.9

4.6 - n×0.2 = 0

4.6 = n×0.2

n = 4.6/0.2 = 23

q = 62 - n = 62 - 23 = 39

so there are 39 quarters and 23 nickels in the jar.

Answer 2

23 nickels, 39 quarters

Explanation:

Let x = the number of quarters

Let y = the number of nickels

x + y = 62 x = 62 - y

.25x + .05y = 10.90

Multiply both sides of the equation by 100 to get rid of the decimal points.

25x + 5y = 1090

25(62-y) + 5y = 1090

1550 - 25y + 5y = 1090

1550 - 1550 - 25y + 5y = 1090 - 1550

-20y = -460

-20y / -20 = -460 / -20

y = 23 nickels

x = 62 - y

x = 62 - 23

x = 39 quarters