A piece of ribbon 2000 cm long is cut into 3 parts, A, B and C.
A is 4 times as long as B.
C is 160 cm shorter than B.
Give the answers in cm.
- How much longer is A than B?
- What is the total length of A and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 160
Length of A = 4 x (1 u + 160) = 4 u + 640
Total length of A, B and C
= 4 u + 640 + 1 u + 160 + 1 u
= 4 u + 1 u + 1 u + 640 + 160
= 6 u + 800
6 u + 800 = 2000
6 u = 2000 - 800
6 u = 1200
1 u = 1200 ÷ 6 = 200
Length of A longer than B
= 4 u + 640 - (1 u + 160)
= 4 u - 1 u + 640 - 160
= 3 u + 480
= 3 x 200 + 480
= 600 + 480
= 1080 cm
(b)
Total length of A and C
= 4 u + 640 + 1 u
= 5 u + 640
= 5 x 200 + 640
= 1000 + 640
= 1640 cm
Answer(s): (a) 1080 cm; (b) 1640 cm