A piece of ribbon 3400 cm long is cut into 3 parts, C, B and A.
C is 3 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 = 3 x (1 u + 300) = 3 u + 900
Total length of C, B and A
= 3 u + 900 + 1 u + 300 + 1 u
= 3 u + 1 u + 1 u + 900 + 300
= 5 u + 1200
5 u + 1200 = 3400
5 u = 3400 - 1200
5 u = 2200
1 u = 2200 ÷ 5 = 440
Length of C longer than B
= 3 u + 900 - (1 u + 300)
= 3 u - 1 u + 900 - 300
= 2 u + 600
= 2 x 440 + 600
= 880 + 600
= 1480 cm
(b)
Total length of C and A
= 3 u + 900 + 1 u
= 4 u + 900
= 4 x 440 + 900
= 1760 + 900
= 2660 cm
Answer(s): (a) 1480 cm; (b) 2660 cm