A piece of ribbon 4200 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 280 cm shorter than C.
Give the answers in cm.
- How much shorter is A than B?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 280
Length of B = 3 x (1 u + 280) = 3 u + 840
Total length of B, C and A
= 3 u + 840 + 1 u + 280 + 1 u
= 3 u + 1 u + 1 u + 840 + 280
= 5 u + 1120
5 u + 1120 = 4200
5 u = 4200 - 1120
5 u = 3080
1 u = 3080 ÷ 5 = 616
Length of A shorter than B
= 3 u + 840 - 1 u
= 3 u - 1 u + 840
= 2 u + 840
= 2 x 616 + 840
= 1232 + 840
= 2072 cm
(b)
Total length of B and C = 3 u + 840 + 1 u + 280
= 3 u + 1 u + 840 + 280
= 4 x 616 + 1120 = 2464 + 1120 = 3584 cm Answer(s): (a) 2072 cm; (b) 3584 cm