Am I doing this right? The question is... At the first store Arlene visited, she spent 40% of her money plus $4. At the second store she spent 50% of her remaining money plus $5. At the third store Arlene spent 60% of her remaining money plus $6. When Arlene finished shopping at the three stores, she had $2 left over. How many dollars did she have when she started shopping? My equation was x - 2 = ((0.4x+4)0.5+5)0.6+6. Both sides of the equation were to find how much she spent. I got 13.86363...

9514 1404 393

  $90

Step-by-step explanation:

Let's consider the remaining money. If x represents the amount Arlene started with, then the remaining amounts are ...

  after first store: x -(0.4x +4) = 0.60x -4

After spending 50% of her money, the amount remaining will be 1-50% = 50%. Then spending 5 more dollars reduces the amount remaining by another 5.

  after second store: (0.60x -4)(0.50) -5 = 0.30x -2 -7 = 0.30x -7

After spending 60% of her money, the amount remaining will be 1-60% = 40%. Then spending 6 more dollars reduces the amount remaining by another 6.

  after third store: (0.30x -7)(0.40) -6 = 0.12x -2.80 -6 = 0.12x -8.80

This is reported to be $2, so we have ...

  0.12x -8.80 = 2

  0.12x = 10.80

  x = 90

Arlene started shopping with $90.

Check

At the first store, Arlene spent 0.40×$90 +$4 = $40, so she had $90-40=$50 remaining.

At the second store, Arlene spent 0.50×$50 +$5 = $30, so she had $50-30=$20 remaining.

At the third store, Arlene spent 0.60×$20+$6 = $18, so she had $20-18 =$2 remaining.

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