SOLUTION: Jill buys 16 cookies, Bella buys 12 cookies, and Catharine buys ‘x’ cookies. The average number of cookies the three of them bought is between 19 and 23, inclusive. What is the

Algebra ->  Finance -> SOLUTION: Jill buys 16 cookies, Bella buys 12 cookies, and Catharine buys ‘x’ cookies. The average number of cookies the three of them bought is between 19 and 23, inclusive. What is the      Log On


   

Question 1195151: Jill buys 16 cookies, Bella buys 12 cookies, and Catharine buys ‘x’ cookies. The average number of cookies the three of them bought is between 19 and 23, inclusive. What is the smallest number of cookies Catharine could have bought?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

I came after @josgarithmetic to write the solution in correct form.


19%3C=%2816%2B12%2Bx%29%2F3%3C=23


57%3C=x%2B28%3C=69

29%3C=x%3C=41

highlight%28x=29%29



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There is no need to work with compound inequalities, as both of the other tutors did. The smallest number of cookies Catherine could have bought means the average number of cookies is the smallest possible, which is 19. So

%2816%2B12%2Bx%29%2F3=19
28%2Bx=57
x=29

ANSWER: 29

Note another way to find the answer, in a problem like this where all the numbers are close together, is to use the given average to balance the "overs" and "unders".

The average is to be 19. 16 is 3 below that average, and 12 is 7 below that average; so those two together are a total of 10 below the average. That means the third number needs to be 10 above the average.

So again the answer is the same: 19+10 = 29.