A piece of ribbon 2400 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 130 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 + 130
Length of A = 3 x (1 u + 130) = 3 u + 390
Total length of A, C and B
= 3 u + 390 + 1 u + 130 + 1 u
= 3 u + 1 u + 1 u + 390 + 130
= 5 u + 520
5 u + 520 = 2400
5 u = 2400 - 520
5 u = 1880
1 u = 1880 ÷ 5 = 376
Length of B shorter than A
= 3 u + 390 - 1 u
= 3 u - 1 u + 390
= 2 u + 390
= 2 x 376 + 390
= 752 + 390
= 1142 cm
(b)
Total length of A and C = 3 u + 390 + 1 u + 130
= 3 u + 1 u + 390 + 130
= 4 x 376 + 520 = 1504 + 520 = 2024 cm Answer(s): (a) 1142 cm; (b) 2024 cm