Word Problem

Question

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

Answer 1

Step 1. Convert board to cm (2.5m=250cm).

 

Step 2. Write all equations.
Total length (add each shelf): s₁+s₂+s₃+s₄=250
s₂=2*s₁+18

s₃=s₁-12

s₄=s₁+4

 

Step 3. Substitute each shelf into the total length equation

s₁+(2*s₁+18)+(s₁-12)+(s₁+4)=250

 

Step 4. Simplify the equation and solve for s₁.

 

Step 5. Substitute s₁ to solve for s₂.

 

[Hint: You answer should be a bit bigger than 100 cm.]