SOLUTION: "Two dump trucks have capacities of 10 tons and 12 tons. They make a total of 20 round trips to haul 226 tons of topsoil for a landscaping project. How many round trips does each t

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: "Two dump trucks have capacities of 10 tons and 12 tons. They make a total of 20 round trips to haul 226 tons of topsoil for a landscaping project. How many round trips does each t      Log On


   

Question 338448: "Two dump trucks have capacities of 10 tons and 12 tons. They make a total of 20 round trips to haul 226 tons of topsoil for a landscaping project. How many round trips does each truck make?"
I just need help with setting up the system, I can do the rest.
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2By=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%2B12y=226


So you have the system


system%28x%2By=20%2C10x%2B12y=226%29


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%2By=20 Start with the first equation


y=20-x Subtract x from both sides


y=-x%2B20 Rearrange the equation


Since y=-x%2B20, we can now replace each y in the second equation with -x%2B20 to solve for x



10x%2B12highlight%28%28-x%2B20%29%29=226 Plug in y=-x%2B20 into the second equation. In other words, replace each y with -x%2B20. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



10x%2B%2812%29%28-1%29x%2B%2812%29%2820%29=226 Distribute 12 to -x%2B20


10x-12x%2B240=226 Multiply


-2x%2B240=226 Combine like terms on the left side


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


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


x=%28-14%29%2F%28-2%29 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%2B20 (remember we previously solved for y in the first equation).



y=-x%2B20 Start with the equation where y was previously isolated.


y=-%287%29%2B20 Plug in x=7


y=-7%2B20 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.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website.

Jim