A piece of ribbon 3800 cm long is cut into 3 parts, B, A and C.
B is 3 times as long as A.
C is 160 cm shorter than A.
Give the answers in cm.
- How much longer is B than A?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of A = 1 u + 160
Length of B = 3 x (1 u + 160) = 3 u + 480
Total length of B, A and C
= 3 u + 480 + 1 u + 160 + 1 u
= 3 u + 1 u + 1 u + 480 + 160
= 5 u + 640
5 u + 640 = 3800
5 u = 3800 - 640
5 u = 3160
1 u = 3160 ÷ 5 = 632
Length of B longer than A
= 3 u + 480 - (1 u + 160)
= 3 u - 1 u + 480 - 160
= 2 u + 320
= 2 x 632 + 320
= 1264 + 320
= 1584 cm
(b)
Total length of B and C
= 3 u + 480 + 1 u
= 4 u + 480
= 4 x 632 + 480
= 2528 + 480
= 3008 cm
Answer(s): (a) 1584 cm; (b) 3008 cm