A piece of ribbon 4100 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 160 cm shorter than B.
Give the answers in cm.
- How much longer is C than B?
- What is the total length of C and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 160
Length of C = 3 x (1 u + 160) = 3 u + 480
Total length of C, B and A
= 3 u + 480 + 1 u + 160 + 1 u
= 3 u + 1 u + 1 u + 480 + 160
= 5 u + 640
5 u + 640 = 4100
5 u = 4100 - 640
5 u = 3460
1 u = 3460 ÷ 5 = 692
Length of C longer than B
= 3 u + 480 - (1 u + 160)
= 3 u - 1 u + 480 - 160
= 2 u + 320
= 2 x 692 + 320
= 1384 + 320
= 1704 cm
(b)
Total length of C and A
= 3 u + 480 + 1 u
= 4 u + 480
= 4 x 692 + 480
= 2768 + 480
= 3248 cm
Answer(s): (a) 1704 cm; (b) 3248 cm