An art store offers prints in two sizes. The store earns $15 on each small print sold and $25 on each large print sold. The owner needs to make a daily profit of at least $700 in order to cover costs. Due to equipment limitations, the number of small prints made must be more than three times the number of large prints. Given that x represents the number of small prints sold and y represents the number of large prints sold, determine which inequalities represent the constraints for this situation. x + y ≤ 60 15x + 25y 3y 15x + 25y ≥ 700 y > 3x x + 3y ≥ 60 Which combinations of small prints and large prints satisfy this system? (45,10) (35,15) (30,10) (40,5)

Question

Mathematics

Abraham Fernandez

30 April, 14:51

An art store offers prints in two sizes. The store earns $15 on each small print sold and $25 on each large print sold. The owner needs to make a daily profit of at least $700 in order to cover costs. Due to equipment limitations, the number of small prints made must be more than three times the number of large prints. Given that x represents the number of small prints sold and y represents the number of large prints sold, determine which inequalities represent the constraints for this situation. x + y ≤ 60 15x + 25y 3y 15x + 25y ≥ 700 y > 3x x + 3y ≥ 60 Which combinations of small prints and large prints satisfy this system? (45,10) (35,15) (30,10) (40,5)

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Answers (1)

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Jasmin Kaiser · Answer 1

The answer definitely 15x + 25y > = 700 for the inequality. So the number of small prints is more than 3 times the large prints. We can also have here the number of small prints : x = 3y. So the equation we have is 15 (3y) + 25y > = 700. We take the least amount to solve:

15 (3y) + 25y = 700

=> 45y + 25y = 700

=> 70y = 700

=> y = 10.

So the amount of large prints is 10

The amount of small prints is 10x3 = 30

So it would be (30,10)