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 280 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 + 280
Length of B = 3 x (1 u + 280) = 3 u + 840
Total length of B, A and C
= 3 u + 840 + 1 u + 280 + 1 u
= 3 u + 1 u + 1 u + 840 + 280
= 5 u + 1120
5 u + 1120 = 4000
5 u = 4000 - 1120
5 u = 2880
1 u = 2880 ÷ 5 = 576
Length of B longer than A
= 3 u + 840 - (1 u + 280)
= 3 u - 1 u + 840 - 280
= 2 u + 560
= 2 x 576 + 560
= 1152 + 560
= 1712 cm
(b)
Total length of B and C
= 3 u + 840 + 1 u
= 4 u + 840
= 4 x 576 + 840
= 2304 + 840
= 3144 cm
Answer(s): (a) 1712 cm; (b) 3144 cm