A piece of ribbon 4100 cm long is cut into 3 parts, A, C and B.
A is 2 times as long as C.
B is 180 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 + 180
Length of A = 2 x (1 u + 180) = 2 u + 360
Total length of A, C and B
= 2 u + 360 + 1 u + 180 + 1 u
= 2 u + 1 u + 1 u + 360 + 180
= 4 u + 540
4 u + 540 = 4100
4 u = 4100 - 540
4 u = 3560
1 u = 3560 ÷ 4 = 890
Length of B shorter than A
= 2 u + 360 - 1 u
= 2 u - 1 u + 360
= 1 u + 360
= 1 x 890 + 360
= 890 + 360
= 1250 cm
(b)
Total length of A and C = 2 u + 360 + 1 u + 180
= 2 u + 1 u + 360 + 180
= 3 x 890 + 540 = 2670 + 540 = 3210 cm Answer(s): (a) 1250 cm; (b) 3210 cm