A piece of ribbon 3700 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 280 cm shorter than B.
Give the answers in cm.
- How much shorter is A than C?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 280
Length of C = 3 x (1 u + 280) = 3 u + 840
Total length of C, B and A
= 3 u + 840 + 1 u + 280 + 1 u
= 3 u + 1 u + 1 u + 840 + 280
= 5 u + 1120
5 u + 1120 = 3700
5 u = 3700 - 1120
5 u = 2580
1 u = 2580 ÷ 5 = 516
Length of A shorter than C
= 3 u + 840 - 1 u
= 3 u - 1 u + 840
= 2 u + 840
= 2 x 516 + 840
= 1032 + 840
= 1872 cm
(b)
Total length of C and B = 3 u + 840 + 1 u + 280
= 3 u + 1 u + 840 + 280
= 4 x 516 + 1120 = 2064 + 1120 = 3184 cm Answer(s): (a) 1872 cm; (b) 3184 cm