Question

Brody and his children went into a bakery and where they sell cookies for $1 each and brownies for $1.50 each. Brody has $15 to spend and must buy no less than 11 cookies and brownies altogether. If x represents the number of cookies purchased and y represents the number of brownies purchased, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

8 brownies and 3 cookies

Explanation:

B + C》11

1.5B + C《15

C = 11 - B

1.5B + 11 - B = 15

0.5B = 4

B = 8

C = 11 - 8 = 3

Verification:

B + C》11

8 + 3》11

11》11

1.5B + C《15

1.5(8) + 3》15

12 + 3》15

15》15

Verified

Answer 2

x+y ≥11

1x + 1.5 y ≤15

7 cookies and 5 brownies

Explanation:

x = number of cookies

y = number of brownies

x+y ≥11

1x + 1.5 y ≤15

Putting each inequality in slope intercept form

y ≥11 -x

1x + 1.5 y ≤15

1.5 y ≤ -x +15

1.5 y/1.5 ≤ -x/1.5 +15/1.5

y ≤ -2/3x +10

graphing( see attached graph)

We can buy 7 cookies and 5 brownies

Check

7+5 ≥11 check

1*7 + 1.5 *5 ≤15

7 +7.5

14.5 < 15 check