A piece of ribbon 1100 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 180 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 + 180
Length of C = 3 x (1 u + 180) = 3 u + 540
Total length of C, B and A
= 3 u + 540 + 1 u + 180 + 1 u
= 3 u + 1 u + 1 u + 540 + 180
= 5 u + 720
5 u + 720 = 1100
5 u = 1100 - 720
5 u = 380
1 u = 380 ÷ 5 = 76
Length of A shorter than C
= 3 u + 540 - 1 u
= 3 u - 1 u + 540
= 2 u + 540
= 2 x 76 + 540
= 152 + 540
= 692 cm
(b)
Total length of C and B = 3 u + 540 + 1 u + 180
= 3 u + 1 u + 540 + 180
= 4 x 76 + 720 = 304 + 720 = 1024 cm Answer(s): (a) 692 cm; (b) 1024 cm