Sam has $175.00 to spend on shirts and DVDs. The shirts he wants are expensive and cost $30 each. Suppose DVDs are $12 each. Write and solve the inequality that models this situation using x for the number of shirts and y for the number of DVDs.

x=number of shirts

y=number of DVDs

We can suggest the following system of inequalities.

30x+12y<175

We solve for x:

maxmimun number of y: y<175/12; y<14

30x+12y<175

30x<175-12y

x< (175-12 y) / 30 " y" can be:0,1,2, ...,14

Answer 1 = the solution for shirts would be x< (175-12y) / 30;

"y " can be:0,1,2, ...,14

We solve for y;

maximum number of DVDs: x<175/30<5

30x+12y<175

12y<175-30x

y< (175-30x) / 12; "x" can be: 0,1,2,3,4,5.

answer 2: the solutions for DVDs would be: y< (175-30x) / 12;

"x" can be: 0,1,2,3,4,5.

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