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

1 m = 100 cm....so 2.5 m = (2.5 * 100) = 250 cm

a = 1st shelf
b = 2nd
c = 3rd
d = 4th

a + b + c + d = 250
b = 2a + 18
c = a - 12
d = a + 4

a + (2a + 18) + (a - 12) + (a + 4) = 250
5a + 10 = 250
5a = 250 - 10
5a = 240
a = 240/5
a = 48 cm <== 1st shelf

b = 2a + 18 = 2(48) + 18 = 114 cm <== 2nd shelf
c = a - 12 = 48 - 12 = 36 cm <== 3rd shelf
d = a + 4 = 48 + 4 = 52 cm <== 4th shelf

so 2nd shelf is 114 cm

Answer 2

The equation I created for this was 250 cm= x + 2x + 18 + x-12 + x+ 4 where x is the length of the first shelf. I then simplified my equation to this:

250= 5x +10. Then I used algebra to find x (if you need me to explain, just leave a comment please). For this one, x= 48cm.

Then, I multiplied 48 by two and added 18. This gave me an answer of 114cm for the length for the length of the second shelf.