A piece of ribbon 4900 cm long is cut into 3 parts, A, C and B.
A is 3 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 = 3 x (1 u + 250) = 3 u + 750
Total length of A, C and B
= 3 u + 750 + 1 u + 250 + 1 u
= 3 u + 1 u + 1 u + 750 + 250
= 5 u + 1000
5 u + 1000 = 4900
5 u = 4900 - 1000
5 u = 3900
1 u = 3900 ÷ 5 = 780
Length of B shorter than A
= 3 u + 750 - 1 u
= 3 u - 1 u + 750
= 2 u + 750
= 2 x 780 + 750
= 1560 + 750
= 2310 cm
(b)
Total length of A and C = 3 u + 750 + 1 u + 250
= 3 u + 1 u + 750 + 250
= 4 x 780 + 1000 = 3120 + 1000 = 4120 cm Answer(s): (a) 2310 cm; (b) 4120 cm