A piece of ribbon 2200 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 160 cm shorter than B.
Give the answers in cm.
- How much shorter is C than A?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 160
Length of A = 3 x (1 u + 160) = 3 u + 480
Total length of A, B and C
= 3 u + 480 + 1 u + 160 + 1 u
= 3 u + 1 u + 1 u + 480 + 160
= 5 u + 640
5 u + 640 = 2200
5 u = 2200 - 640
5 u = 1560
1 u = 1560 ÷ 5 = 312
Length of C shorter than A
= 3 u + 480 - 1 u
= 3 u - 1 u + 480
= 2 u + 480
= 2 x 312 + 480
= 624 + 480
= 1104 cm
(b)
Total length of A and B = 3 u + 480 + 1 u + 160
= 3 u + 1 u + 480 + 160
= 4 x 312 + 640 = 1248 + 640 = 1888 cm Answer(s): (a) 1104 cm; (b) 1888 cm