A jar contains 30 coins. Th ere are only nickels and quarters in the jar. If the total amount of money in the jar is $3.90 how many quarters and nickels are there in the jar

Answer 1

I'm going to deal in cents to svoid those pesky decimals.

n + q = 30

5n + 25q = 390

First, solve the first equation for either n or q. I'll do n.

n + q - q = 30 - q

n = 30 - q

Now, we can swap any expression for any expression on either side of the =, because equal meeeeeeans they are the same. Since n and 30 - q are the same, I can swap out 30 - q for n in the 2nd equation.

5(30 - q) + 25q = 390

150 - 5q + 25q = 390

150 + 20q - 150 = 390 - 150

20q = 240

20q/20 = 240/20

q = 12 quarters

n = 30 - q

n = 30 - 12

n = 18 nickles

Now we have to check our work.

25(12) + 5(18) = 390

300 + 90 = 390

390 = 390

0 = 0

Boom.