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at the grocery store a cucumber costs $0.33 and a green pepper costs $0.52. what combination of cucumbers and green peppers could you buy for exactly $5.00

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3 Answers

We start with equation 0.52x+0.33y=5    <=>   52x+33y=500. y intercept is (0, 500/33), x intercept is (500/52,0). 500/33<15.16 and 500/52<9.62. X  values are from the set of the whole numbers {0,1,2,3,4,5,6,7,8,9}, y values are from the set of whole numbers {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}. Substitute x values into the linear function. For value x=2  we solve y=12 and it is only value which result    whole number for y. solution is 12 cucumbers and 2 green pappers.  
Rewrite the requirement as 33C+52G=500
I tried to get as close to  a multiple of 100 as I could with 33 and to fill in with 52
12×33=396 and 2×52=104.  12 cucumber and 2 green peppers works perfectly.
0.33 C + 0.52G = 5    Have to solve it for integer values of C & G
 
$3.00 on G Pepper.                             $3/0.52 = 5.76  number of Gl pepper
 $ 2.00 on  Cucumbers                          $2/ 0.33 = 6.06
 
                                                         (6 C) ($0.33) + 5 ($ 0.52) = 4.58  / $.42 left from $5
                                                          $0.42 - $0.33 = 0.09/  $0.09 left.
 
                                                7 cucumber, and 5 Green Pepper is the best combination.