A piece of ribbon 3200 cm long is cut into 3 parts, C, A and B.
C is 2 times as long as A.
B is 300 cm shorter than A.
Give the answers in cm.
- How much shorter is B than C?
- What is the total length of C and A?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 300
Length of C = 2 x (1 u + 300) = 2 u + 600
Total length of C, A and B
= 2 u + 600 + 1 u + 300 + 1 u
= 2 u + 1 u + 1 u + 600 + 300
= 4 u + 900
4 u + 900 = 3200
4 u = 3200 - 900
4 u = 2300
1 u = 2300 ÷ 4 = 575
Length of B shorter than C
= 2 u + 600 - 1 u
= 2 u - 1 u + 600
= 1 u + 600
= 1 x 575 + 600
= 575 + 600
= 1175 cm
(b)
Total length of C and A = 2 u + 600 + 1 u + 300
= 2 u + 1 u + 600 + 300
= 3 x 575 + 900 = 1725 + 900 = 2625 cm Answer(s): (a) 1175 cm; (b) 2625 cm