An algebra word problem. Please help!

Question

Bianca went to the mall with her friends. She spent 2/3 of her money on make-up. Then she spent 1/3 of her remaining money at a clothing store. After that she went home and had $8 left. How much money did she have at the beginning?

Answer 1

Hi Sam,

 

The best way to solve this is by looking at the final value that you know and working backwards.

 

You know that Bianca went home and had $8 left. This was after spending 1/3 of her money at the clothing store. So, $8 was 2/3 of the money she had when she went to the clothing store. If $8 was 2/3 of the money she had when she went to the clothing store, it means she had $12 when she went to the clothing store.

 

Working further backwards, the question indicates that before she had gone to the clothing store she spent money on make-up. Because the question indicates she spent 2/3 of her money on make-up, then the $12 she took to the clothing store (from the previous paragraph) would be 1/3 of the money she had before buying make-up. If $12 is 1/3 of the money she had before buying any make-up, it means she had $36 at the beginning, when she first went to the mall.

 

Started the day:

$36

 

Spent 2/3 of her money on make-up:

So, she spent 2/3 of $36

So, she spent $24

 

Then she had $12 left ($36 - $24)

 

Spent 1/3 of her remaining money at a clothing store:

So, she spent 1/3 of $12

So, she spent $4

 

Then she had $8 left.

 

 

Hope this helps!

Answer 2

Hi, Sam

Okay, so let's call Bianca's beginning balance X.

 

So, if she spent 2/3 on makeup, she had (1/3)x left.

Then, she spent 1/3 of that at the clothing store.

So, she had 2/3 of that left. So now she has (2/3) x (1/3)X  = (2/9)X

If (2/9)X = 8 dollars

multiply both sides by 9:

2X = 72

X = 36 dollars

 

She began with $36