A piece of ribbon 3700 cm long is cut into 3 parts, C, A and B.
C is 3 times as long as A.
B is 300 cm shorter than A.
Give the answers in cm.
- How much longer is C than A?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 300
Length of C = 3 x (1 u + 300) = 3 u + 900
Total length of C, A and B
= 3 u + 900 + 1 u + 300 + 1 u
= 3 u + 1 u + 1 u + 900 + 300
= 5 u + 1200
5 u + 1200 = 3700
5 u = 3700 - 1200
5 u = 2500
1 u = 2500 ÷ 5 = 500
Length of C longer than A
= 3 u + 900 - (1 u + 300)
= 3 u - 1 u + 900 - 300
= 2 u + 600
= 2 x 500 + 600
= 1000 + 600
= 1600 cm
(b)
Total length of C and B
= 3 u + 900 + 1 u
= 4 u + 900
= 4 x 500 + 900
= 2000 + 900
= 2900 cm
Answer(s): (a) 1600 cm; (b) 2900 cm