A piece of ribbon 3000 cm long is cut into 3 parts, A, C and B.
A is 4 times as long as C.
B is 210 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 + 210
Length of A = 4 x (1 u + 210) = 4 u + 840
Total length of A, C and B
= 4 u + 840 + 1 u + 210 + 1 u
= 4 u + 1 u + 1 u + 840 + 210
= 6 u + 1050
6 u + 1050 = 3000
6 u = 3000 - 1050
6 u = 1950
1 u = 1950 ÷ 6 = 325
Length of B shorter than A
= 4 u + 840 - 1 u
= 4 u - 1 u + 840
= 3 u + 840
= 3 x 325 + 840
= 975 + 840
= 1815 cm
(b)
Total length of A and C = 4 u + 840 + 1 u + 210
= 4 u + 1 u + 840 + 210
= 5 x 325 + 1050 = 1625 + 1050 = 2675 cm Answer(s): (a) 1815 cm; (b) 2675 cm