# 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?

Posted on

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

Posted on

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.

Posted on

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

Posted on

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

Posted on

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.