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Math word problem.Two dump trucks have capacities of 10 tons and 12 tons. They make a...

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bryerbunny9 | Student, Undergraduate | eNotes Newbie

Posted February 6, 2009 at 12:08 PM via web

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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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cburr | Middle School Teacher | (Level 2) Associate Educator

Posted February 7, 2009 at 1:26 AM (Answer #1)

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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

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kmieciakp | High School Teacher | Valedictorian

Posted February 6, 2009 at 1:31 PM (Answer #2)

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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.

 

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mcetner | High School Teacher | (Level 1) Adjunct Educator

Posted February 7, 2009 at 1:38 AM (Answer #3)

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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.

 

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revolution | College Teacher | Valedictorian

Posted September 10, 2010 at 6:32 PM (Answer #4)

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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


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jess1999 | TA , Grade 9 | Valedictorian

Posted July 22, 2014 at 2:56 PM (Answer #5)

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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

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