A piece of ribbon 3400 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 200 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 + 200
Length of B = 3 x (1 u + 200) = 3 u + 600
Total length of B, C and A
= 3 u + 600 + 1 u + 200 + 1 u
= 3 u + 1 u + 1 u + 600 + 200
= 5 u + 800
5 u + 800 = 3400
5 u = 3400 - 800
5 u = 2600
1 u = 2600 ÷ 5 = 520
Length of B longer than C
= 3 u + 600 - (1 u + 200)
= 3 u - 1 u + 600 - 200
= 2 u + 400
= 2 x 520 + 400
= 1040 + 400
= 1440 cm
(b)
Total length of B and A
= 3 u + 600 + 1 u
= 4 u + 600
= 4 x 520 + 600
= 2080 + 600
= 2680 cm
Answer(s): (a) 1440 cm; (b) 2680 cm