A piece of ribbon 1900 cm long is cut into 3 parts, C, A and B.
C is 3 times as long as A.
B is 270 cm shorter than A.
Give the answers in cm.
- How much shorter is B than C?
- What is the total length of C and A?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 270
Length of C = 3 x (1 u + 270) = 3 u + 810
Total length of C, A and B
= 3 u + 810 + 1 u + 270 + 1 u
= 3 u + 1 u + 1 u + 810 + 270
= 5 u + 1080
5 u + 1080 = 1900
5 u = 1900 - 1080
5 u = 820
1 u = 820 ÷ 5 = 164
Length of B shorter than C
= 3 u + 810 - 1 u
= 3 u - 1 u + 810
= 2 u + 810
= 2 x 164 + 810
= 328 + 810
= 1138 cm
(b)
Total length of C and A = 3 u + 810 + 1 u + 270
= 3 u + 1 u + 810 + 270
= 4 x 164 + 1080 = 656 + 1080 = 1736 cm Answer(s): (a) 1138 cm; (b) 1736 cm