A delivery truck is transporting boxes of two sizes: large and small.

Question

A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 60 pounds each, and the small boxes weigh 20 pounds each. There are 120 boxes in all. If the truck is carrying a total of 4600 pounds in boxes, how many of each type of box is it carrying?

Number of large boxes:

Number of small boxes:

Answer 1

Start by pulling out the known and unknown information from the problem's description:

Knowns:

1) One large box weighs 60 lbs

2) One small box weighs 20 lbs

3) The truck has 120 boxes total

4) The truck currently weighs 4600 lbs

Unknowns:

1) The number of large boxes on the truck

2) The number of small boxes on the truck

We want to solve for two unknown pieces of information: in order to this, we can make a system of equations. The number of equations we need should be equal to the number of unknowns we have. In that case, we need to make 2 equations using the information we were given.

Start by associating two variables: one for each box we know of.

Let L = large box

Let S = small box

Let's make our first equation. We know we have 120 boxes total. We know that whatever amount of small boxes and large boxes we have, they should add up to 120 in this case. Let's put that in equation form:

L + S = 120 (Equation 1)

All we need is our second equation now. We know the weight per large box and the weight per small box. Whatever amount of large and small boxes we have, we know their weight has to add to the weight of the truck, 4600 lbs. To make an equation, we just multiply the weights of each box by their variables to find the total weights each, and then set that equal to the weight of the truck:

20*S + 60*L = 4600 (Equation 2)

We finally have the equations we need to solve. We can either choose to use substitution or termination to isolate the variables we have to find their actual values. When solved, we should have the following answers:

S = 65

L = 55

Remember we have to label our answers with units since those answers relate to the variables we associated small and large boxes with.

Therefore:

The truck carries 65 small boxes and 55 large boxes.

Hope this helps!

Answer 2

This problem is a system of equations. By the information given we can write two equations.

Let L = the number of Large boxes.

Let S = the number of Small boxes.

so we can write that the total number of boxes (120) is equal to the number of large boxes plus the number of small boxes.

L + S = 120

The total weights of the boxes (4600) together is equal to the weight of the sum of the total of large boxes plus the weight of the sum of the total number of small boxes.

one Large box weights 60 ponds & one Small box weights 20 pounds.

60*L + 20*S = 4600

so our two equations are:

L + S = 120

60*L + 20*S = 4600

We can use the elimination method by eliminating one of the variables and solving for the other.

60*L + 20*S = 4600

L + S = 120 <<<<. Lets get rid of L by multiplying this equation by -60

-60*(L + S = 120)

Our system of equations looks like this now,

60*L + 20*S = 4600.

-60*L -60*S = -7200. Now we just add vertically,

0 - 40*S = - 2600

S = -2600/(-40). >>> S = 65

We can plug S back into one of our equations.

L + S = 120 >>>> L + (65) = 120

L = 120 - 65

L = 55

So L = 55 and S = 65

We can double check our work by plugging our answers back in and seeing if we get the right results.

55 + 65 = 120 >> correct

60*(55) + 20*(65) = 4600 >>> 3300 + 1300 = 4600 >> correct

We can confirm that L = 55 and S = 65

Answer 3

For this problem you will want to set up a system of equations.

1. For the first equation, you want to think of the relationship in terms of pounds. The large boxes are 60 pounds and the smaller boxes are 20 pounds. You also know that total, the boxes are 4600 pounds. This means your first equation will be:
2. 60x + 20y = 4600
3. x=number of large boxes
4. y=number of small boxes
5. For the second equation, you want to think about number of boxes. You know you have 120 total, so your equation will be:
6. x + y = 120
7. Now you can use substitution to solve your system of equations. You will want to solve for either x or y first. I chose x.
8. x = 120 - y (subtracting y from both sides)
9. Plug what you got for x into equation number 1.
10. 60 (120 - y) + 20y = 4600
11. Simplify and solve for y
12. 7200 - 40y = 4600
13. -40y = -2600
14. y = 65
15. Plug your answer for y back into equation 2. Solve for x.
16. x + 65 = 120
17. x= 55

Number of large boxes= 55

Number of small boxes= 65

Answer 4

Solve the system

60 L + 20 S = 4600

L + S = 120 multiply by -20

60L + 20S =4600

-20L - 20S = -2400

40L = 2200 divide by 40

L = 55 substitute to find S