Question 338448
Let x = # of trips the 10 ton truck makes and y = # of trips that the 12 ton truck makes



So if "They make a total of 20 round trips ", then {{{x+y=20}}}. In addition, if "Two dump trucks have capacities of 10 tons and 12 tons" and they need "to haul 226 tons of topsoil" this means that {{{10x+12y=226}}}



So you have the system 



{{{system(x+y=20,10x+12y=226)}}}



You can stop here if you want, but I figured I'd finish anyway.



Now let's solve the system by use of substitution.




In order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.



So let's isolate y in the first equation


{{{x+y=20}}} Start with the first equation



{{{y=20-x}}}  Subtract {{{x}}} from both sides



{{{y=-x+20}}} Rearrange the equation



Since {{{y=-x+20}}}, we can now replace each {{{y}}} in the second equation with {{{-x+20}}} to solve for {{{x}}}




{{{10x+12highlight((-x+20))=226}}} Plug in {{{y=-x+20}}} into the second equation. In other words, replace each {{{y}}} with {{{-x+20}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{10x+(12)(-1)x+(12)(20)=226}}} Distribute {{{12}}} to {{{-x+20}}}



{{{10x-12x+240=226}}} Multiply



{{{-2x+240=226}}} Combine like terms on the left side



{{{-2x=226-240}}}Subtract 240 from both sides



{{{-2x=-14}}} Combine like terms on the right side



{{{x=(-14)/(-2)}}} Divide both sides by -2 to isolate x



{{{x=7}}} Divide



Since we know that {{{x=7}}} we can plug it into the equation {{{y=-x+20}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+20}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(7)+20}}} Plug in {{{x=7}}}



{{{y=-7+20}}} Multiply



{{{y=13}}} Combine like terms 



So our answers are:


{{{x=7}}} and {{{y=13}}}



This means that the 10 ton truck has to make 7 trips while the 12 ton truck has to make 13 trips.



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Jim