Question

A delivery truck is transporting boxes of two sizes: large and small. The large box weighs 60 pounds each, and the small box weighs 30 pounds each. There are 125 boxes in all. If the truck is carrying a total of 5700 pounds in boxes, how many of each type of box is it carrying

Answer 1

There are 65 60-lb boxes and 60 30-lb boxes.

Explanation:

Method:

Define two variables for the two unknowns. Set up a system of two equations in two variables. One equation deals with the numbers of boxes. The other equation deals with the weights. Solve the system of equations.

Define variables:

Let x = number of 60-lb boxes.

Let y = number of 30-lb boxes.

Equation dealing with numbers of boxes:

The total number of boxes is x + y. We are told the total number of boxes is 125, so the first equation is:

x + y = 125

Equation dealing with weights:

x number of 60-lb boxes weight 60x.

y number of 30-lb boxes weight 30y.

The total weight of all boxes is 60x + 30y. We are told the total weight is 5700 lb. The second equation is:

60x + 30y = 5700

System of two equations in two variables:

x + y = 125

60x + 30y = 5700

Solution of the system of equations by the substitution method:

Solve the first equation for x:

x + y = 125

Subtract y from both sides.

x = 125 - y

Substitute 125 - y for x in the second original equation.

60x + 30y = 5700

60(125 - y) + 30y = 5700

Distribute the 60.

7500 - 60y + 30y = 5700

Combine y-terms on left side.

7500 - 30y = 5700

Subtract 7500 from both sides.

-30y = -1800

Divide both sides by -30.

y = 60

There are 60 30-lb boxes.

Now substitute 60 for y in the first original equation and solve for x.

x + y = 125

x + 60 = 125

Subtract 60 from both sides.

x = 65

There are 65 60-lb boxes.

Answer: There are 65 60-lb boxes and 60 30-lb boxes.

Check:

The given information is there there are 125 boxes, and the total weight is 5700 lb.

The total number of boxes is 65 boxes + 60 boxes = 125 boxes. This checks with the given information.

The total weight is

65 * 60 lb + 60 * 30 lb = 3900 lb + 1800 lb = 5700 lb

This checks with the given information.

Our solution is correct.

Answer 2

60 small boxes and 65 large boxes

Explanation:

From the given information we can make two equations:

L + S = 125

60L + 30S = 5700

S represents the number of small boxes and L represents the number of large boxes.

To solve an equation we need there to be only one variable, so I solved for s in the first equation.

L + S = 125

S = 125 - L

Now I can plug this into the second equation

60L + 30S = 5700

60L + 30(125 - L) = 5700 (substitute S)

60L + 3750 - 30L = 5700

30L + 3750 = 5700 (combine like terms)

30L = 1950 (subtract 3750 from both sides)

L = 65 (divide both sides by 30)

Now that we know there are 65 larger boxes, plug in 65 for L to find S.

S = 125 - L

S = 125 - 65

S = 60

So there are 65 large boxes and 60 small boxes