Got confused, was never good at algebra. . .

Question

A photography shop has a self-service photo center that allows you to make prints of pictures. Each sheet of printed pictures costs $8. The number of pictures that fit on each is shown. (Four 3 inch by 5-inch pictures fit on one sheet. Two four by six-inch pictures fit on one sheet.) 

A. You want at least 16 pictures of any size, and you are willing to spend up to $48. Write and graph a system of inequalities that models the situation. 

B. Will you be able to purchase 12 pictures that are 3 inches by 5 inches and six pictures that are four by six inches? explain

 

Answer 1

A)

 

Let the # of 3-in by 5-in = x

Let the # of 4-in by 6-in = y

 

Now that we defined our variables, we can set up a system of inequalities.

 

x + y ≥ 16                     ineq1   -----> total number of sheets

8(4x + 2y) ≤ 48             ineq2   -----> total cost of sheets

4x + 2y ≤ 6                  

2x + y ≤ 3                     eq2

 

Rewriting the equation,

 

y ≥ -x + 16                      ineq1

y ≤ -2x + 3                      ineq2

 

Graph these inequalities on a coordinate system.  Shade the regions.  The overlapping shaded region is the solution set.

 

Note: the overlapping shaded region should strictly be in the first quadrant.

 

 

B)

 

Use the solution set to answer this question.