A piece of ribbon 1700 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 280 cm shorter than B.
Give the answers in cm.
- How much shorter is C than A?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 280
Length of A = 2 x (1 u + 280) = 2 u + 560
Total length of A, B and C
= 2 u + 560 + 1 u + 280 + 1 u
= 2 u + 1 u + 1 u + 560 + 280
= 4 u + 840
4 u + 840 = 1700
4 u = 1700 - 840
4 u = 860
1 u = 860 ÷ 4 = 215
Length of C shorter than A
= 2 u + 560 - 1 u
= 2 u - 1 u + 560
= 1 u + 560
= 1 x 215 + 560
= 215 + 560
= 775 cm
(b)
Total length of A and B = 2 u + 560 + 1 u + 280
= 2 u + 1 u + 560 + 280
= 3 x 215 + 840 = 645 + 840 = 1485 cm Answer(s): (a) 775 cm; (b) 1485 cm