A piece of ribbon 2900 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 120 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 + 120
Length of C = 3 x (1 u + 120) = 3 u + 360
Total length of C, B and A
= 3 u + 360 + 1 u + 120 + 1 u
= 3 u + 1 u + 1 u + 360 + 120
= 5 u + 480
5 u + 480 = 2900
5 u = 2900 - 480
5 u = 2420
1 u = 2420 ÷ 5 = 484
Length of C longer than B
= 3 u + 360 - (1 u + 120)
= 3 u - 1 u + 360 - 120
= 2 u + 240
= 2 x 484 + 240
= 968 + 240
= 1208 cm
(b)
Total length of C and A
= 3 u + 360 + 1 u
= 4 u + 360
= 4 x 484 + 360
= 1936 + 360
= 2296 cm
Answer(s): (a) 1208 cm; (b) 2296 cm