A piece of ribbon 1700 cm long is cut into 3 parts, C, B and A.
C is 2 times as long as B.
A is 160 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 + 160
Length of C = 2 x (1 u + 160) = 2 u + 320
Total length of C, B and A
= 2 u + 320 + 1 u + 160 + 1 u
= 2 u + 1 u + 1 u + 320 + 160
= 4 u + 480
4 u + 480 = 1700
4 u = 1700 - 480
4 u = 1220
1 u = 1220 ÷ 4 = 305
Length of C longer than B
= 2 u + 320 - (1 u + 160)
= 2 u - 1 u + 320 - 160
= 1 u + 160
= 1 x 305 + 160
= 305 + 160
= 465 cm
(b)
Total length of C and A
= 2 u + 320 + 1 u
= 3 u + 320
= 3 x 305 + 320
= 915 + 320
= 1235 cm
Answer(s): (a) 465 cm; (b) 1235 cm