Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer. Would 5 trees be a solution to the inequality in part b? Justify your answer.

Answer 1

r = tons of rock
t = number of trees
r≥30 to cover yard
c = 60 r + 84 t ≤2500
if I use the minimum amount of rock (30 tons) then I can use the maximum number of trees so
r = 30
60 * 30 + 84 t ≤ 2500
1800 + 84 t ≤ 2500
84 t ≤ 700
t ≤ 8
so 5 trees is a solution