A piece of ribbon 5000 cm long is cut into 3 parts, A, C and B.
A is 5 times as long as C.
B is 250 cm shorter than C.
Give the answers in cm.
- How much shorter is B than A?
- What is the total length of A and C?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of C = 1 u + 250
Length of A = 5 x (1 u + 250) = 5 u + 1250
Total length of A, C and B
= 5 u + 1250 + 1 u + 250 + 1 u
= 5 u + 1 u + 1 u + 1250 + 250
= 7 u + 1500
7 u + 1500 = 5000
7 u = 5000 - 1500
7 u = 3500
1 u = 3500 ÷ 7 = 500
Length of B shorter than A
= 5 u + 1250 - 1 u
= 5 u - 1 u + 1250
= 4 u + 1250
= 4 x 500 + 1250
= 2000 + 1250
= 3250 cm
(b)
Total length of A and C = 5 u + 1250 + 1 u + 250
= 5 u + 1 u + 1250 + 250
= 6 x 500 + 1500 = 3000 + 1500 = 4500 cm Answer(s): (a) 3250 cm; (b) 4500 cm