Sofia's family is opening a Tex-Mex restaurant soon, and Sofia wants to serve homemade salsa. She plans to grow a combination of pepper plants and tomato plants in her garden. Each pepper plant needs 3 square feet of space, and each tomato plant needs 8 square feet. The garden has an area of 500 square feet.
Which pairs (p,t) represent possible numbers of pepper plants and tomato plants Sofia could grow?
a) (20,55)
b) (100,25)
c) (10,60)
d) (200, - 15)
Let p be the number of pepper plants and t be the number of tomato plants Sofia could grow.
The total square feet taken up by the pepper plants would be 3p, and the total square feet taken up by the tomato plants would be 8t.
According to the problem, the total square feet available in the garden is 500.
So, the equation representing the total square feet taken up by the plants would be: 3p + 8t = 500.
To check which pairs (p,t) represent possible numbers of pepper plants and tomato plants Sofia could grow, we need to simply test each pair in the equation.
a) (20,55)
3(20) + 8(55) = 60 + 440 = 500 ✅
b) (100,25)
3(100) + 8(25) = 300 + 200 = 500 ✅
c) (10,60)
3(10) + 8(60) = 30 + 480 = 510 ❌
d) (200,-15)
Not a possible combination as the number of tomato plants cannot be negative.
Therefore, the possible pairs represent number of pepper plants and tomato plants Sofia could grow are:
a) (20,55)
b) (100,25)