Answer:
The answer is order pairs (5 , 12) and (4 , 9)
Explanation:
* Lets change the story problem to some inequalities and check
these them from the graph and after find the correct answer
- The money Luis can spend is $240
- The cost of each men's shirt is $8
- The cost of each women's shirt is $12
- The number of the men's shirts is x
- The number of the women's shirts is y
∴ The inequality of the money spend is ⇒ 8x + 12y ≥ 240
- Represented by the line which cross the y-axis at point (0 , 20)
- Luis needs at least 3 men's shirts
∴ The inequality of the number of men's shirted wanted is ⇒ x ≥ 3
- Represented by the vertical line cross the x-axis ate point (3 , 0)
- Luis needs at least 8 women's shirts
∴ The inequality of the number of women's shirted wanted is ⇒ y ≥ 8
- Represented by the horizontal line cross the y-axis ate point (0 , 8)
- The number of women's shirts must be at least twice the number
of the men's shirts
∴ The inequality of this condition is y ≥ 2x
- Represented by the line which passes through the origin point (0 , 0)
* Now the region which represent all this condition together is
the shaded region on the graph, so lets check from the graph
to find the order pairs which meet the all conditions, that
means the points must be lie on the blue region
∵ (5 , 12) is in the blue region
* Lets check from the inequalities:
∵ 8(5) + 12(12) = 184 < 240
∵ 5 > 3 and 12 > 8
∵ 12 > 2(5)
∴ (5 , 12) meets all the conditions
- (7 , 13) is out the blue region
∵ (4 , 9) is in the blue region
* Lets check from the inequalities:
∵ 8(4) + 12(9) = 140 < 240
∵ 4 > 3 and 9 > 8
∵ 9 > 2(4)
∴ (4 , 9) meets all the conditions
- (2 , 15) is out the blue region