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

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Question 190595: 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.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Cost of rocks: 30*$60 = $1800

So 30 rocks cost $1,800


Now let x=# of trees


So the price of the total number of trees is 84x (multiply the number of trees "x" by the price per tree of $84)


So their sum will be 1800%2B84x which means that the total cost is 1800%2B84x dollars.


Now set the total cost less than or equal to the total budget:

1800%2B84x%3C=2500


Now let's solve for "x":



1800%2B84x%3C=2500 Start with the given inequality.


84x%3C=2500-1800 Subtract 1800 from both sides.


84x%3C=700 Combine like terms on the right side.


x%3C=%28700%29%2F%2884%29 Divide both sides by 84 to isolate x.


x%3C=25%2F3 Reduce.


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Answer:

So the answer is x%3C=25%2F3


Which approximates to x%3C=8.333


So this means that you can buy at most 8 trees (ie no more than 8 trees) to stay within budget.