A piece of ribbon 2900 cm long is cut into 3 parts, C, B and A.
C is 4 times as long as B.
A is 250 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 + 250
Length of C = 4 x (1 u + 250) = 4 u + 1000
Total length of C, B and A
= 4 u + 1000 + 1 u + 250 + 1 u
= 4 u + 1 u + 1 u + 1000 + 250
= 6 u + 1250
6 u + 1250 = 2900
6 u = 2900 - 1250
6 u = 1650
1 u = 1650 ÷ 6 = 275
Length of A shorter than C
= 4 u + 1000 - 1 u
= 4 u - 1 u + 1000
= 3 u + 1000
= 3 x 275 + 1000
= 825 + 1000
= 1825 cm
(b)
Total length of C and B = 4 u + 1000 + 1 u + 250
= 4 u + 1 u + 1000 + 250
= 5 x 275 + 1250 = 1375 + 1250 = 2625 cm Answer(s): (a) 1825 cm; (b) 2625 cm