A piece of ribbon 3200 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 shorter is C than A?
- What is the total length of A and B?
(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 = 3200
6 u = 3200 - 800
6 u = 2400
1 u = 2400 ÷ 6 = 400
Length of C shorter than A
= 4 u + 640 - 1 u
= 4 u - 1 u + 640
= 3 u + 640
= 3 x 400 + 640
= 1200 + 640
= 1840 cm
(b)
Total length of A and B = 4 u + 640 + 1 u + 160
= 4 u + 1 u + 640 + 160
= 5 x 400 + 800 = 2000 + 800 = 2800 cm Answer(s): (a) 1840 cm; (b) 2800 cm