# Math word problem.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...

Math word problem.

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?

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In case it would be helpful, I'm going to annotate the previous answer so you know what bryerbunny was doing.

Let x= truck

*Actually, x is the number of round trips made by the 10 ton truck and y is the number of round trips made by the 12 ton truck. *

x + y = 20

*We know from the problem that if you add together the number of round trips made by each truck, you get the 20 trip total.*

x= 20-y

*This is just math to isolate x. So, now we can substitute "20-y" for x in the equation and it will be easier to solve.*

10 (20-y) + 12y = 226

*This equation reflects how much topsoil each truck carried. Truck x (which is '20-y' now) carried 10 tons on each of its round trips, and truck y carried 12 tons per trip. [Note that even though it's a round trip, they only carried soil in one direction.]*

200-10y + 12y = 226

*This step and the ones that follow are just math steps to simplify the equation. This one turns 10(20-y) into 200 - 10y*

2(100-5y+6y)=226

*This is one way to further simplify by pulling 2 out from each part of the left hand side. *

2(100+y) = 226

*This is just showing that -5y + 6y is the same as 1y or just y*

100 + y = 113

y= 13

x = 7

Step 1: define variables: let x = the number of trips the 10 ton truck makes, and let y = the number of trips the 12 ton truck makes.

Step 2: write equations: total number of trips: x + y = 20. Total number of tons: 10x + 12y = 226 (10 tons for each x, and 12 tons for each y makes total 226.)

Step 3: Solve the system: There are many ways to do this, I will use elimination. x + y = 20, 10x + 12y = 226. Multiply the first equation by -10, and -10x + -10y = -200. Add the equations together, and 0x + 2y = 26, or 2y = 26. Divide by 2 and y = 13 trips. Plug back in to the first equation, and x + 13 = 20. Solve, and x = 7 trips.

Step 4: answer the question. The truck that can hole 10 tons makes 7 trips, and the truck that can hold 12 tons makes 13 trips.

First , " x " = truck

So use the equation

x + y = 20 subtract " y " on both sides

By subtracting " y " on both sides , you should get

x = 20 - y

Now use

10 ( 20 - y ) + 12y = 226 distribute the 10

By distributing the 10 , you should get

200 - 10y + 12y = 226 combine the like terms

By combining the like terms , you should get

200 + 2y = 226 now subtract both sides by 200

By subtracting , you should get

2y = 26 Divide both sides by 2 .

By dividing both sides by 2 , you should get

y = 13

Now plug 13 into x + y = 20

x + 13 = 20 subtract both sides by 13 .

By subtracting both sides by 13 , you should get

x = 7

So your answer is x = 7 and y = 13

Let x be the rounds trip that first truck make and y be the rounds trip the second truck make

x+y=20- eqn 1

Two dump trucks have capacities of 10 tons and 12 tons and they need to haul 226 tons of topsoil for a landscaping project, so:

10x+12y=226- eqn 2

Make X the subject, so X=20-y- eqn 3

Sub. eqn 3 to eqn 2

10(20-y)+12y=226

200-10y+12y=226

2y+200=226

2y=26

y=13

Sub. y=13 to eqn 1

x+13=20

x=20-13

= 7

**First truck make 7 round trips while next truck make 13 round trips**

Let x= truck

x + y = 20

x= 20-y

10 (20-y) + 12y = 226

200 -10y + 12y = 226

2(100-5y+6y)=226

2(100+y) = 226

100 + y = 113

y= 13

x = 7

Check:

70 + 13(12)

70 + 156

226

done.