A piece of ribbon 3100 cm long is cut into 3 parts, C, B and A.
C is 5 times as long as B.
A is 120 cm shorter than B.
Give the answers in cm.
- How much shorter is A than C?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 120
Length of C = 5 x (1 u + 120) = 5 u + 600
Total length of C, B and A
= 5 u + 600 + 1 u + 120 + 1 u
= 5 u + 1 u + 1 u + 600 + 120
= 7 u + 720
7 u + 720 = 3100
7 u = 3100 - 720
7 u = 2380
1 u = 2380 ÷ 7 = 340
Length of A shorter than C
= 5 u + 600 - 1 u
= 5 u - 1 u + 600
= 4 u + 600
= 4 x 340 + 600
= 1360 + 600
= 1960 cm
(b)
Total length of C and B = 5 u + 600 + 1 u + 120
= 5 u + 1 u + 600 + 120
= 6 x 340 + 720 = 2040 + 720 = 2760 cm Answer(s): (a) 1960 cm; (b) 2760 cm