A piece of ribbon 2000 cm long is cut into 3 parts, C, B and A.
C is 2 times as long as B.
A is 300 cm shorter than B.
Give the answers in cm.
- How much longer is C than B?
- What is the total length of C and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 300
Length of C = 2 x (1 u + 300) = 2 u + 600
Total length of C, B and A
= 2 u + 600 + 1 u + 300 + 1 u
= 2 u + 1 u + 1 u + 600 + 300
= 4 u + 900
4 u + 900 = 2000
4 u = 2000 - 900
4 u = 1100
1 u = 1100 ÷ 4 = 275
Length of C longer than B
= 2 u + 600 - (1 u + 300)
= 2 u - 1 u + 600 - 300
= 1 u + 300
= 1 x 275 + 300
= 275 + 300
= 575 cm
(b)
Total length of C and A
= 2 u + 600 + 1 u
= 3 u + 600
= 3 x 275 + 600
= 825 + 600
= 1425 cm
Answer(s): (a) 575 cm; (b) 1425 cm