How many blouses bought?

Question

Raychel used 3/8 of her money to buy blouses and 2/5 of the remainder to buy 2 pairs of pants. A pair of Pants costs 3 times as much as  a blouse. How many blouses did she buy

Answer 1

Hi Joseph,

This is a cool problem.

 

First, we should define some variables:

Let X = total amount of money before any purchases.

Let b = the number of blouses purchased and B = the price of a blouse.

Let p = the number of pants purchased (2) and P = the price of pants.

 

OK, first sentence, "Raychel used 3/8 of her money to but blouses . . . this means that

(3/8)X = bB         CALL THIS EQUATION 1    

(bB is the amount spent on blouses - how many blouses times the price of each blouse)

 

Next part . . . "and 2/5 of the remainder to buy 2 pairs of pants."

If she spent (3/8)X on blouses, then (5/8)X remains . . . and 2/5 of that amount is 2/5 (5/8)X = (10/40)X = (1/4)X

 

So, (1/4)X was spent on pants.  This means that

(1/4)X = 2P        CALL THIS EQUATION 2

(2P is the amount spent on pants - 2 pants times the price of each pair of pants)

 

Last part . . . a pair of pants costs 3 times as much as a blouse.

So, P = 3B      CALL THIS EQUATION 3

 

Now we just have to do some substitutions . . .

Equation 2 has a P, replace it with 3B (from equation 3)

 

(1/4)X = 2P

(1/4)X = 2(3B)

(1/4)X = 6B

 

Multiply both sides by 4 and 

X = 24B

 

Replace the X in Equation 1 with 24 B

 

(3/8)X = bB

(3/8)(24B) = bB

72B/8 = bB

9B = bB

9  = b

 

Raychel bought 9 blouses.

 

Hope this helps!  I had fun!  :)