You are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $12 each. You have a budget of $300 for the shirts. The equation 10x+12y=300 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.

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MrRoyal MrRoyal · Answer 1 · 2020-10-23T07:16:25+02:00

Question:

a. Graph the equation.

b. Twelve students decide they want short-sleeved shirts. How many long-sleeved shirts can you order.

Answer:

See attachment for graph

12 long-sleeved shirts

Step-by-step explanation:

Given

[tex]10x + 12y = 300[/tex]

Plotting the graph:

Set x = 0

[tex]10(0) + 12y = 300[/tex]

[tex]12y = 300[/tex]

[tex]y = 300/12[/tex] --- divide through by 12

[tex]y = 25[/tex]

Set x = 0

[tex]10x + 12(0) = 300[/tex]

[tex]10x = 300[/tex]

[tex]x = 300/10[/tex] --- divide through by 10

[tex]x = 30[/tex]

So, the graph will be plotted using: (0, 25) and (30, 0)

See attachment for graph

Determine y when x = 12

[tex]10x + 12y = 300[/tex]

[tex]10(12) + 12y = 300[/tex]

[tex]120 +12y = 300[/tex]

[tex]12y = 300 - 120[/tex] --- collect like terms

[tex]12y = 180[/tex]

[tex]y = 180/12[/tex] -- solve for y

[tex]y = 15[/tex]