A piece of ribbon 3800 cm long is cut into 3 parts, A, C and B.
A is 2 times as long as C.
B is 160 cm shorter than C.
Give the answers in cm.
- How much longer is A than C?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of C = 1 u + 160
Length of A = 2 x (1 u + 160) = 2 u + 320
Total length of A, C and B
= 2 u + 320 + 1 u + 160 + 1 u
= 2 u + 1 u + 1 u + 320 + 160
= 4 u + 480
4 u + 480 = 3800
4 u = 3800 - 480
4 u = 3320
1 u = 3320 ÷ 4 = 830
Length of A longer than C
= 2 u + 320 - (1 u + 160)
= 2 u - 1 u + 320 - 160
= 1 u + 160
= 1 x 830 + 160
= 830 + 160
= 990 cm
(b)
Total length of A and B
= 2 u + 320 + 1 u
= 3 u + 320
= 3 x 830 + 320
= 2490 + 320
= 2810 cm
Answer(s): (a) 990 cm; (b) 2810 cm