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

Algebra ->  Inequalities -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

1)
x=money you spend
:
:
%246000+%3C=+x+%3C=+%2410000
:
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
x%3C=8
:

Answer by jim_thompson5910(35256) About Me  (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 30%2A60=1800. 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 84x.


Now add the two costs to get 1800%2B84x. Rearrange the expression to get 84x%2B1800



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 84x%2B1800 is less than or equal to 2500 like this

84x%2B1800%3C=2500


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Solving the Inequality:


84x%2B1800%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


If we round down, we get x%3C=8 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.