word problem Alegebra 1

Question

If Jane has 36 coins totaling $3.00, and the coins are all nickels and quarters, how many of each coin does she have?

Answer 1

Here's another problem requiring solution with a system of equations.

We know that there only two types of coins, nickels and quarters and we know the monetary value of each (I hope!).

Total value is (0.05) x no. nickels (N) + (0.25) x no. quarters (Q) = $3.00

0.05 N + 0.25 Q = 3.00

(Could also do this in cents if you don't like decimals: 5 N + 25 Q = 300)

We also know that N + Q = 36 coins. Lets solve for N. N = 36 - Q Then substitute for N in the value equation.

0.05(36 - Q) + 0.25 Q = 3.00 Use distribution rule 1.8 - 0.05 Q + 0.25 Q = 3.00

1.8 + 0.20 Q = 3.00 -> 0.20 Q = 1.20 -> Q = 6 (nice when answer is a whole no., otherwise something's wrong!)

If Q is 6, then N must be 36 - 6 = 30 Answer: 30 Nickels and 6 quarters

Check: 30 + 6 = 36 coins

0.05 (30) + 0.25 (6) = 1.50 + 1.50 = $3.00