PLEASE DO NOT USE ALGEBRA (If it is possible, you can use trial and error).

Question

A bottle of shampoo and a bottle of body wash cost $14.50 in all. Mrs. Diaz

buys 3 bottles of shampoo and 5 bottles of body wash for $56.90.

a) What is the cost of one bottle of shampoo?

 

 

b) If Mrs. Diaz pays $46.80 for some bottles of shampoo, how many bottles of shampoo does she buy?

 

Answer 1

This is called "elimination."

 

               "A bottle of shampoo and a bottle of body wash cost $14.50 in all."

 

(5 times)   5 bottles of shampoo and 5 bottles of body wash for $72.50

               "3 bottles of shampoo and 5 bottles of body wash for $56.90"

subtract: ----------------------------------------------------------------------  

                2 bottles of shampoo                                         for $15.60

 

divide by2 :  1 bottle of shampoo                                              $7.80

 

 

 

b) If Mrs. Diaz pays $46.80 for some bottles of shampoo, how many bottles of shampoo does she buy?

        $46.80 / $7.80 = 6 bottles of shampoo

Answer 2

An edit based on Asok B.'s comment:

 

a bottle of shampoo and a bottle of wash is $14.50.

Therefore

3 bottles of shampoo and 3 bottles of wash is $43.50

That means

2 bottles of wash are $13.40 ($56.90-$43.50), or $6.70 each.

 

Can yow say how much the shampoo costs?

Answer 3

One bottle of shampoo + one bottle of body wash = 14.50 

3 bottles of shampoo and 5 bottles of body wash cost  $56.90.

Rewriting, 3 bottles of shampoo + 3 bottles of body wash + 2 bottles of body wash = 56.90

 So, 3x 14.50 +2 bottles of body wash = 56.90

thus, 2 bottles of body wash cost  56.90- 3x(14.50)  = 56.90 - 43.50 =  13.40

so the price of one bottle of body wash = 13.40/2 = 6.70

so the price of one bottle of shampoo= 14.50 - 6.70 = 7.80

Answer 4

Start with b)

 

However much a bottle of shampoo costs, it needs to divide evenly into $46.80 (she can't buy a partial bottle of shampoo).

 

You also know that one bottle of shampoo must cost less than $14.50, since the shampoo plus a bottle of body wash costs that much.

 

So starting with $46.80:

If she has two bottles, they would cost $23.40 each, which is more than $14.50, so that doesn't work.

If she has three bottles, they would cost $15.60 each, which is also more than $14.50, so that doesn't work.

If she has four bottles, they would cost $11.70 each, which is less than $14.50, so that might work.

 

If the bottle of shampoo is $11.70, that means the bottle of body wash is $14.50 - $11.70, which is $2.80.

 

To see if this is the right answer, plug these numbers into the equation that 3 bottles of shampoo and 5 bottles of body wash cost $56.90.

So does (3 x $11.70) + (5 x $2.80) equal $56.90?

NO, it equals $49.10, so this must not be the correct answer.

 

Going back, if she has five bottles of shampoo, they would cost $9.36 each.

 

If the bottle of shampoo is $9.36, that means the bottle of body wash is $14.50 - $9.36, which is $5.14.

 

To see if this is the right answer, plug these numbers into the equation that 3 bottles of shampoo and 5 bottles of body wash cost $56.90.

So does (3 x $9.36) + (5 x $5.14) equal $56.90?

NO, it equals $53.78, so this must not be the correct answer either.

 

Going back, if she has six bottles of shampoo, they would cost $7.80 each.

 

If the bottle of shampoo is $7.80, that means the body wash is $14.50 - $7.80, which is $6.70.

 

To see if this is the right answer, plug these numbers into the equation that 3 bottles of shampoo and 5 bottles of body wash cost $56.90.

So does (3 x $7.80) + (5 x $6.70) equal $56.90?

YES

 

So the answer to a) is that one bottle of shampoo costs $7.80

And the answer to b) is that she buys six bottles of shampoo