Problema Solution
You are planning an ornamental garden that has a total area of 200 square feet. There 2 sizes of ornamental plants you have chosen for your gtarden. tach small plant requires 2.5 square feet of space and each large plant requires 8 square feet of space. this situation can be modeled by the equation 2.5x + 8y = 200 where x is the number of small plants and y is the number of large plnats to be place in the garden.
Answer provided by our tutors
Arrange equation in the slope/intercept form
2x + 8y = 200
8y = 200 - 2.5x
y = - x
y = 25 - .3125x
:
Choose values for x that result in a positive integer value for y
Since we divided equation by 8, choose multiples of 8, greater than 8, for x
x=16
y = 25 - .3125(16)
y = 25 - 5
y = 20, 20 large plants and 16 small plants
:
x = 32
y = 25 - .3125(32)
y = 25 - 10
y = 15, 15 large and 32 small
:
x = 48
x = 25 - .3125(48)
x = 25 - 15
y = 10, 10 large and 48 small
:
:
Check solution using the last combination x=48 and y=10:
48(2.5) + 10(8) =
120 + 80 = 200