The amount of money Tom has is 75% of Sally's amount of money after Sally spent $120 and Tom saved all of his money Tom's amount is 50% more than Sally's. how much money did each of them have at the beginning?

To solve this problem, let's break it down step by step:

Step 1: Let's assume Sally's initial amount of money is "x" dollars.

Step 2: After Sally spent $120, her remaining amount of money is (x - 120) dollars.

Step 3: Tom has saved all of his money, which means Tom's amount of money is (x - 120) dollars as well.

Step 4: According to the problem, Tom's amount is 50% more than Sally's amount, which means Tom's amount is 1.5 times Sally's amount.

Step 5: We can write the equation as follows: 1.5(x - 120) = x.

Step 6: Simplify the equation by distributing 1.5: 1.5x - 180 = x.

Step 7: Subtract "x" from both sides to isolate the variable: 1.5x - x = 180.

Step 8: Simplify the equation: 0.5x = 180.

Step 9: Divide both sides by 0.5 to solve for x: x = 180 / 0.5.

Step 10: Calculate x: x = 360.

Therefore, Sally's initial amount of money was $360, and Tom's initial amount of money was also $360.

Tom's amount --- t

Sally's amount --- s

t = .75s --> t = (3/4)s

Sally spends 120 , so she has s - 120
and now:
t = 1.5( s - 120)
t = 1.5s - 180

Then: (3/4)s = 1.5s - 180
3s = 6s - 720
-3s = -720

carry on ....