Box A contained only 50 cent coins while Box B contained only 20 cents coins, Box B has 60 more coins than Box A but the value of all the coins in Box A is $4.50 more than the value of all the coins in Box B. Find the amount of money in Box A.

Question

Please help me to solve this question, thanks so much.

Answer 1

number of coins in box B ---- b , 20 cent pieces
number of coins in box A ---- a , 50 cent pieces

equation dealing with number of coins:
b = a+60

equation dealing with value of coins:
50a - 20b = 450
5a - 2b = 45
use substitution:
5a - 2(a+60) = 45
5a - 2a - 120 = 45
3a = 165
a = 55 , then b = 115

check:
Box A contains 55(50) = $27.50
box B contains 20(115) = $23.00
box A contains 27.50 - 23.00 more , or $4.50
(my answer is correct)