How do I do this problem:
Chelsea sold baked goods to raise money for various charitable organizations. She gave a third of the money raised to the American Red Cross. Then gave a fourth of that money to United Way. THEN gave half of the money to Twin city Missions. If Twin City Missions received $200, how much money did Chelsea have in the beginning?
Let X = beginning amount
I assume that the first two are proportions of the grand total and the last is a proportion of the remainder.
(X - 1/3 X - 1/4 X)/2 = $200
Solve for X.
I hope this helps. Thanks for asking.
To solve this problem, you need to work backward. Since you know that Twin City Missions received $200, you can determine the amount of money Chelsea had before she made her donations.
Let's start by representing the amount of money Chelsea had left after each donation. We'll call the original amount of money she had "x."
After giving a third of the money to the American Red Cross, Chelsea would have 2/3 of the original amount left:
2/3 * x
Next, she gave a fourth of that amount to United Way. Therefore, the amount left after this donation would be:
3/4 * (2/3 * x)
Simplifying the expression further:
3/4 * 2/3 * x = 6/12 * x = 1/2 * x
Finally, it is given that Twin City Missions received $200. So we can set up an equation:
1/2 * x = $200
To solve this equation, we can multiply both sides by 2:
x = $200 * 2
x = $400
Thus, Chelsea had $400 in the beginning.
Note: The above explanation breaks down the problem step by step. However, you can also solve it using the concept of inverses. In this case, you would multiply the amount received by Twin City Missions ($200) by the reciprocals of each fraction multiplier (1/2, 3/4, and 2/3) in reverse order.