A piece of ribbon 4000 cm long is cut into 3 parts, B, A and C.
B is 3 times as long as A.
C is 120 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 + 120
Length of B = 3 x (1 u + 120) = 3 u + 360
Total length of B, A and C
= 3 u + 360 + 1 u + 120 + 1 u
= 3 u + 1 u + 1 u + 360 + 120
= 5 u + 480
5 u + 480 = 4000
5 u = 4000 - 480
5 u = 3520
1 u = 3520 ÷ 5 = 704
Length of B longer than A
= 3 u + 360 - (1 u + 120)
= 3 u - 1 u + 360 - 120
= 2 u + 240
= 2 x 704 + 240
= 1408 + 240
= 1648 cm
(b)
Total length of B and C
= 3 u + 360 + 1 u
= 4 u + 360
= 4 x 704 + 360
= 2816 + 360
= 3176 cm
Answer(s): (a) 1648 cm; (b) 3176 cm