Let's denote the initial number of one dollar coins as 3x and the initial number of fifty cent coins as 4x.
After 6 one dollar coins were removed and the same amount of fifty cent coins were added, the new ratio of one dollar coins to fifty cent coins became 1:3. This means that the number of one dollar coins is now 1(3x-6) and the number of fifty cent coins is 3(4x+6).
Setting up the equation:
(3x-6)/(4x) = 1/3
3(3x-6) = 4(4x+6)
9x - 18 = 16x + 24
9x - 16x = 24 + 18
-7x = 42
x = -6
Since x is negative, this means that our initial assumption was incorrect. We need to reverse the initial numbers: 3x becomes -3 and 4x becomes -4.
Total amount of money in the box at the beginning:
3(-3) + 4(-4) = -9 - 16 = $25
Therefore, the total amount of money in the box was $25.
The ratio of one dollar coins to fifty cent coins on a box was 3:4
6 one dollar coins were removed and some fifty cent coins of the same amount were added. The ratio of one dollar coins to fifty cent coins then became 1:3. What was the total amount of money in the box?
1 answer