SOLUTION: You are planning an ornamental garden that has a total area of 200 square feet. There are two sizes of ornamental plants you have chosen for your garden. Each small plant require

Question 174463This question is from textbook Algebra 2, Texas Edition
: You are planning an ornamental garden that has a total area of 200 square feet. There are two sizes of ornamental plants you have chosen for your garden. Each 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 where x is the number of small plants and y is the number of large plants to be placed in the garden. What are three possible numbers of small plants and large plants that you can plant in the garden? This question is from textbook Algebra 2, Texas Edition

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You are planning an ornamental garden that has a total area of 200 square feet. There are two sizes of ornamental plants you have chosen for your garden. Each 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 plants to be placed in the garden. What are three possible numbers of small plants and large plants that you can plant in the garden?
:
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
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