A piece of ribbon 1200 cm long is cut into 3 parts, B, C and A.
B is 4 times as long as C.
A is 300 cm shorter than C.
Give the answers in cm.
- How much longer is B than C?
- What is the total length of B and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 300
Length of B = 4 x (1 u + 300) = 4 u + 1200
Total length of B, C and A
= 4 u + 1200 + 1 u + 300 + 1 u
= 4 u + 1 u + 1 u + 1200 + 300
= 6 u + 1500
6 u + 1500 = 1200
6 u = 1200 - 1500
6 u = -300
1 u = -300 ÷ 6 = -50
Length of B longer than C
= 4 u + 1200 - (1 u + 300)
= 4 u - 1 u + 1200 - 300
= 3 u + 900
= 3 x -50 + 900
= -150 + 900
= 750 cm
(b)
Total length of B and A
= 4 u + 1200 + 1 u
= 5 u + 1200
= 5 x -50 + 1200
= -250 + 1200
= 950 cm
Answer(s): (a) 750 cm; (b) 950 cm