SOLUTION: 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

Question 175463: 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 solver. Express your answer as an inequality and explain how you arrived at your answer.
Found 2 solutions by Mathtut, jim_thompson5910:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!

1)
x=money you spend
:
:

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2) 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 $2500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
:
:
30(60)=price of 30 tons of rocks
2500-[30(60)]=budget left for trees
{2500-[30(60)]}/84=maximum amount of trees you can buy
:
1800=price of 30 tons of rock
2500-1800=700 (budget left for trees)
700/84=8.33333 (maximum amount of trees, before rounding)
Maximum amount of trees you can buy=8

:

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=number of trees

Since "You need 30 tons of rock" and "each ton cost $60", this means that the total cost of the rocks is . So the rocks will cost you $1,800

Now because "each tree is $84" and we let "x" be the number of trees, this means that the total cost of the trees is .

Now add the two costs to get . Rearrange the expression to get

Since you have a "budget for rock and trees of $2,500", this means that you can spend anything less than or equal to $2,500 (nothing higher). So algebraically, this means that the total cost is less than or equal to 2500 like this

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Solving the Inequality:

Start with the given inequality.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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Answer:

So the answer is

Which approximates to

If we round down, we get which means that the number of trees is less than or equal to 8. So you can buy at most 8 trees to stay within budget.
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