A piece of ribbon 2700 cm long is cut into 3 parts, C, B and A.
C is 2 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 = 2 x (1 u + 280) = 2 u + 560
Total length of C, B and A
= 2 u + 560 + 1 u + 280 + 1 u
= 2 u + 1 u + 1 u + 560 + 280
= 4 u + 840
4 u + 840 = 2700
4 u = 2700 - 840
4 u = 1860
1 u = 1860 ÷ 4 = 465
Length of A shorter than C
= 2 u + 560 - 1 u
= 2 u - 1 u + 560
= 1 u + 560
= 1 x 465 + 560
= 465 + 560
= 1025 cm
(b)
Total length of C and B = 2 u + 560 + 1 u + 280
= 2 u + 1 u + 560 + 280
= 3 x 465 + 840 = 1395 + 840 = 2235 cm Answer(s): (a) 1025 cm; (b) 2235 cm