A piece of ribbon 1100 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 250 cm shorter than B.
Give the answers in cm.
- How much shorter is C than A?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 250
Length of A = 3 x (1 u + 250) = 3 u + 750
Total length of A, B and C
= 3 u + 750 + 1 u + 250 + 1 u
= 3 u + 1 u + 1 u + 750 + 250
= 5 u + 1000
5 u + 1000 = 1100
5 u = 1100 - 1000
5 u = 100
1 u = 100 ÷ 5 = 20
Length of C shorter than A
= 3 u + 750 - 1 u
= 3 u - 1 u + 750
= 2 u + 750
= 2 x 20 + 750
= 40 + 750
= 790 cm
(b)
Total length of A and B = 3 u + 750 + 1 u + 250
= 3 u + 1 u + 750 + 250
= 4 x 20 + 1000 = 80 + 1000 = 1080 cm Answer(s): (a) 790 cm; (b) 1080 cm