Question

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.

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)