A piece of ribbon 3100 cm long is cut into 3 parts, C, B and A.
C is 5 times as long as B.
A is 260 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 + 260
Length of C = 5 x (1 u + 260) = 5 u + 1300
Total length of C, B and A
= 5 u + 1300 + 1 u + 260 + 1 u
= 5 u + 1 u + 1 u + 1300 + 260
= 7 u + 1560
7 u + 1560 = 3100
7 u = 3100 - 1560
7 u = 1540
1 u = 1540 ÷ 7 = 220
Length of A shorter than C
= 5 u + 1300 - 1 u
= 5 u - 1 u + 1300
= 4 u + 1300
= 4 x 220 + 1300
= 880 + 1300
= 2180 cm
(b)
Total length of C and B = 5 u + 1300 + 1 u + 260
= 5 u + 1 u + 1300 + 260
= 6 x 220 + 1560 = 1320 + 1560 = 2880 cm Answer(s): (a) 2180 cm; (b) 2880 cm