Question

Matt and Trey are remodeling their gardens. Matt purchased 8 ferns and 1 rosebush for $35. Trey purchased 4 ferns and 3 rosebushes for $25. Determine the price of each plant.

Answer 1

• rosebush: $3
• fern: $4

Explanation:

If we let f and r represent the costs of a fern and a rosebush, respectively, we can write equations that represent each of the purchases:

8f +r = 35 . . . . Matt's purchase

4f +3r = 25 . . . . Trey's purchase

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We can solve these equations using "elimination." We note that the coefficient of f in the second equation is half that in the first equation.

Subtracting the first equation from twice the second, we get ...

2(4f +3r) -(8f +r) = 2(25) -(35)

5r = 15 . . . . . simplify

r = 3 . . . . . . . divide by 5

Substituting into the first equation, we have ...

8f + 3 = 35

8f = 32 . . . . . . subtract 3

f = 4 . . . . . . . . divide by 8

The fern costs $4; the rosebush costs $3.