A piece of ribbon 2300 cm long is cut into 3 parts, C, B and A.
C is 2 times as long as B.
A is 180 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 + 180
Length of C = 2 x (1 u + 180) = 2 u + 360
Total length of C, B and A
= 2 u + 360 + 1 u + 180 + 1 u
= 2 u + 1 u + 1 u + 360 + 180
= 4 u + 540
4 u + 540 = 2300
4 u = 2300 - 540
4 u = 1760
1 u = 1760 ÷ 4 = 440
Length of C longer than B
= 2 u + 360 - (1 u + 180)
= 2 u - 1 u + 360 - 180
= 1 u + 180
= 1 x 440 + 180
= 440 + 180
= 620 cm
(b)
Total length of C and A
= 2 u + 360 + 1 u
= 3 u + 360
= 3 x 440 + 360
= 1320 + 360
= 1680 cm
Answer(s): (a) 620 cm; (b) 1680 cm