Madeleine saved her allowance for 4 months to buy a new game. She spent 1/4 of her money on the game and 1/2 of the remaining money on another toy. If she brought 4 cool erasers for $2.15 each and had $8.90 left, how much did she save in 4 months?
To figure out how much Madeleine saved in 4 months, let's break down the problem step by step.
1. Madeleine spent 1/4 of her money on a game. Let's call the total amount of money she saved "M".
- After buying the game, she had 3/4 of her money left. Therefore, the amount of money she had remaining after buying the game is (3/4)M.
2. Madeleine then spent 1/2 of the remaining money on another toy. Let's update the remaining amount of money she had after buying the game, calling it "R".
- After buying the toy, she had 1/2 of the remaining money left. Therefore, the new amount of money she had remaining is (1/2)R.
3. Madeleine bought 4 cool erasers for $2.15 each. The total cost of the erasers is given as $8.90.
- Let's calculate the total cost of the erasers: 4 * $2.15 = $8.60.
- Subtracting the cost of erasers from the new remaining amount, we get: (1/2)R - $8.60 = $8.90.
Now we can solve the equation:
(1/2)R - $8.60 = $8.90
First, we'll add $8.60 to both sides of the equation to isolate (1/2)R:
(1/2)R = $8.90 + $8.60
Simplifying the right side:
(1/2)R = $17.50
Next, we'll multiply both sides of the equation by 2 to solve for R:
R = $17.50 * 2
R = $35
Since R represents the remaining amount of money Madeleine had after buying the game, and that amount is 3/4 of the total money saved, we can set up another equation:
(3/4)M = $35
To solve for M, we can divide both sides of the equation by (3/4):
M = $35 / (3/4)
Dividing decimals can be tricky, so we need to remember that dividing by a fraction is the same as multiplying by its reciprocal:
M = $35 * (4/3)
Simplifying the right side:
M = $140 / 3
M ≈ $46.67
Therefore, Madeleine saved approximately $46.67 in 4 months.