Robert and his shelves

Question

Robert needs to cut four shelves from a board that is 3 meters long. The first shelf can be represented by x. The second shelf is 15 centimeters longer than the first shelf. The third shelf is 25 centimeters longer than the first shelf. The fourth shelf is twice as long as the first shelf. If Robert must use the entire 3 meter board for the shelves, what is the length of the second shelf, in centimeters?

Answer 1

x+ x+15 + x+25 + 2x = 300

5x = 300-40 = 260

x = 260/5 = 52

x+15 = 67 cm = the 2nd shelf's length

Answer 2

Hello, Jayden,

I'll use the letters a, b, c, and d to represent the four shelf lengths that are to be cut from the 3 meter board. Assign the lengths as described in the question, using x as the length of shelf a. All units here will be in cm.

a: x

b: x+15

c: x+25

d: 2*x

We know that a+b+c+d = 3 meters

Since there are 100cm/meter, we can convert this to 300 cm.

a+b+c+d = 300 cm

Now substitute the four shelf lenghts:

(x)+(x+15)+(x+25)+(2*x) = 300

5x + 40 = 300

x = 52 cm

a: 52cm

b: 67cm

c: 77cm

d: 104cm

300cm

The SECOND shelf is 67cm.

Bob

Answer 3

Use the Segment Addition Postulate. Since the shelves are measured in centimeters and board length is in meters, let's convert the board from 3 m to 300 cm.

|----------|--------------|-----------------|--------------|

x x+15 x+25 2x

<------------------- 300 cm ----------------------->

x + x + 15 + x + 25 + 2x = 300

Solve for x. The second shelf is x +15 cm longer. The units are cm.