MATH SOLVE

2 months ago

Q:
# Kevin and Randy Muise have a jar containing 92 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $13.60 How many of each type of coin do they have? The jar contains ____ quarters. The jar contains ____ nickels.

Accepted Solution

A:

Let n = the number of nickles

Let q = the number of quarters

Then for your problem we have

(1) n + q = 43 and

(2) 5*n + 25*q = 100*6.95 (always work in cents to avoid decimal numbers) or

(3) 5*n + 25*q = 695

Now substitute n of (1) into (3) and get

(4) 5*(43 - q) + 25*q = 695 or

(5) 215 - 5*q + 25*q = 695 or

(6) 20*q = 695 - 215 or

(7) 20*q = 480 or

(8) q = 24

Then using (1) we get

(9) n + 24 = 43 or

(10) n = 19

Let's check these values.

Is (.05*19 + .25*24 = 6.95)?

Is (.95 + 6.00 = 6.95)?

Is (6.95 = 6.95)? Yes

Answer: Kevin and Randy have 19 nickles and 24 quarters in the jar.

Let q = the number of quarters

Then for your problem we have

(1) n + q = 43 and

(2) 5*n + 25*q = 100*6.95 (always work in cents to avoid decimal numbers) or

(3) 5*n + 25*q = 695

Now substitute n of (1) into (3) and get

(4) 5*(43 - q) + 25*q = 695 or

(5) 215 - 5*q + 25*q = 695 or

(6) 20*q = 695 - 215 or

(7) 20*q = 480 or

(8) q = 24

Then using (1) we get

(9) n + 24 = 43 or

(10) n = 19

Let's check these values.

Is (.05*19 + .25*24 = 6.95)?

Is (.95 + 6.00 = 6.95)?

Is (6.95 = 6.95)? Yes

Answer: Kevin and Randy have 19 nickles and 24 quarters in the jar.