for every bottles a fourth can be purchased for 3 dollars Allen pays 120 dollars for 16 what was the normal price and how much did he save?

Question

For every 3 bottles a fourth can be purchased for 3$.Allen pays $120 for 16 bottles. What was the normal price. How much did he save?

Answer 1

Let's do this, Jocelyn!

 

Let x = the normal price.

 

If he bought 16 bottles for $120, we know he bought 12 at regular price and 4 at the reduced price. There are 4 groups of 4 in 16, and every fourth bottle is $3.

 

So, we have 12x + 4(3) = 120

 

12x + 12 = 120

 

12x = 108

 

x = 9

 

So, the normal price for a bottle is $9.  If he paid $3 each for four, then he saved $6 per bottle. 6(4) = 24.

 

His total savings is $24.

 

Hope this helps!

Answer 2

Hi Jocelyn,

 

If Allen paid a different price for every fourth bottle, one way to do the problem is to divide the total amount into chunks of 4.

 

$120/4 = $30

 

So he paid $30 for every 4 bottles.  Since you're told he only paid $3 for the fourth one, you can subtract that out.

 

$30 - $3 = $27

 

Then we'll divide that by 3 to find out what he paid for each individual bottle.

 

$27/3 = $9

 

There's your "normal price."

To find out how much he saved, we need to know how many discounted bottles he got.  Since he bought 16 total, and every fourth bottle was discounted, we just need to divide 16 by 4.

 

16/4 = 4

 

Since these discounted bottles only cost $3, the total cost for all of them is

 

4 x $3 = $12

 

But at the regular price of $9 they would have cost

 

4 x $9 = $36

 

So the difference between the two costs tells you how much he saved

 

$36 - $12 = $24