A piece of ribbon 2600 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 210 cm shorter than C.
Give the answers in cm.
- How much shorter is B than A?
- What is the total length of A and C?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of C = 1 u + 210
Length of A = 3 x (1 u + 210) = 3 u + 630
Total length of A, C and B
= 3 u + 630 + 1 u + 210 + 1 u
= 3 u + 1 u + 1 u + 630 + 210
= 5 u + 840
5 u + 840 = 2600
5 u = 2600 - 840
5 u = 1760
1 u = 1760 ÷ 5 = 352
Length of B shorter than A
= 3 u + 630 - 1 u
= 3 u - 1 u + 630
= 2 u + 630
= 2 x 352 + 630
= 704 + 630
= 1334 cm
(b)
Total length of A and C = 3 u + 630 + 1 u + 210
= 3 u + 1 u + 630 + 210
= 4 x 352 + 840 = 1408 + 840 = 2248 cm Answer(s): (a) 1334 cm; (b) 2248 cm