March 2010 Brain Teaser Solution

Amanda went to the mall to buy supplies. She spent 1/2 of what she had plus $2.00 in the first store. Then she went to the second store and spent 1/2 of what she had left plus $1.00. In the third store, she spent 1/2 of what she had left plus $1.00. In the fourth store and last, she spent 1/2 of what she had left. After all of her purchases, she was left with only $3.00. How much money did she start with and how much did she spend in each store?

Amanda started with $64
she spent $34 in store 1
$16 in store 2
$8 is store 3
$3 in store 4

she spent a total of 34 + 16 + 8 + 3 = 61
therefore she has $3 left


After store 1 she has x - (1/2x + 2) which becomes 1/2x -2

then store 2
1/2 of answer 1 - 1

so 1/2(1/2x - 2) - 1

1/4x - 1- 1
so after store 2: 1/4x - 2


then store 3
1/2(1/4x-2) - 1

1/8x - 1- 1

so after store 3:1/8x - 2

then store 4:

1/2(1/8x - 2)

1/16x - 1

this is = 3

1/16x - 1 = 3

add 1 to both sides

1/16x = 4

x = 64

After store 1 she has 1/2(64)-2 = 30
so after store 2: 1/4x - 2 = 1/4(64) - 2 = 14
so after store 3:1/8x - 2 = 1/8(64) -2 = 6
then store 4: 6/2 = 3