Question

Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 centimeters longer than twice the length of the first shelf. The third shelf is 12 centimeters shorter than the first shelf. The remaining shelf is 4 centimeters longer than the first shelf. If Robert must use the entire 2.5 meter board for the shelves, what is the length of the second shelf, in centimeters?

Answer 1

Givens
Let the first shelf = x
Let the second shelf = 2x + 18
Let the third shelf = x - 12
Let the fourth shelf = x + 4

The total must be 2.5 m

Step One
Convert the board length to cm.

1 meter = 100 cm
2.5 meters = x

1/2.5 = 100/x Cross multiply
1*x = 2.5 * 100
x = 250

Step Two
Add all the lengths together and equate them to 250 cm

x + 2x + 18 + x - 12 + x + 4 = 250

Step Three
Gather like terms.
x + 2x + x + x + 18 - 12 + 4 = 250
5x + 10 = 250

Step Four
Solve the remaining equation.
5x + 10 = 250 Subtract 10 from both sides.
5x = 250 - 10
5x = 240 Divide by 5
x = 240 / 5
x = 48

Answers
The first shelf is 48
The second shelf is 2*48 + 18 = 114
The third shelf 48 - 12 = 36
The fourth shelf = 48 + 4 = 52

Check
Does the total = 250 cm
48 + 114 + 36 + 52 =? 250
250 =? 250 and it checks.