Question

An airplane is loaded with cargo and ready to take off. Before it departs, an unknown numberof 8 pound boxes, b, will be taken off the plane and a 600 pound crate will be put on. To keepthe plane in balance, no more than 400 pounds may be taken off the plane. Write an inequalitythat best describes this situation.a. What are the key words or information needed to solve this problem?b. Write an inequality that describes this situation.c. How many 8 pound boxes can be taken off the plane. Work out the problem, showing all steps taken.

Answer 1

5 1/4 times 1/2 = 2.625. As a fraction
2.625 is 2 5/8 because .625 could be drawn out to 625/1000 125 goes into 625 and 1,000 625 divided by 125

Answer 2

a. What are the key words or information needed to solve this problem?

We must define the variable of interest, in this case it is the number of 8-pound boxes.

Let:

x = unknown number of 8 pound boxes

b. Write an inequality that describes this situation.

To keep the plane in balance, no more than 400 pounds may be taken off the plane. So:

a 600 pound crate will be put on:

600lb

an unknown number of 8 pound boxes, b, will be taken off the plane:

600lb - 8lb(x)

no more than 400 pounds may be taken off the plane:

600lb - 8lb(x) ≤ 400

c. How many 8 pound boxes can be taken off the plane. Work out the problem, showing all steps taken.

Let's solve the previous inequality:

600 - 8x ≤ 400

Solve for x:

Add 8x to both sides:

600 - 8x + 8x ≤ 400 + 8x

600 ≤ 400 + 8x

Subtract 400 from both sides:

600 - 400 ≤ 400 + 8x - 400

200 ≤ 8x

Divide both sides by 8:

200/8 ≤ 8x/x

25 ≤ x