Question 175463
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*60=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+84x}}}. Rearrange the expression to get {{{84x+1800}}}




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+1800}}} is less than or equal to 2500 like this


{{{84x+1800<=2500}}}



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Solving the Inequality:



{{{84x+1800<=2500}}} Start with the given inequality.



{{{84x<=2500-1800}}} Subtract {{{1800}}} from both sides.



{{{84x<=700}}} Combine like terms on the right side.



{{{x<=(700)/(84)}}} Divide both sides by {{{84}}} to isolate {{{x}}}. 



{{{x<=25/3}}} Reduce.



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Answer:


So the answer is {{{x<=25/3}}} 



Which approximates to {{{x<=8.333}}} 



If we round down, we get {{{x<=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.