A piece of ribbon 4200 cm long is cut into 3 parts, A, C and B.
A is 5 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 = 5 x (1 u + 210) = 5 u + 1050
Total length of A, C and B
= 5 u + 1050 + 1 u + 210 + 1 u
= 5 u + 1 u + 1 u + 1050 + 210
= 7 u + 1260
7 u + 1260 = 4200
7 u = 4200 - 1260
7 u = 2940
1 u = 2940 ÷ 7 = 420
Length of B shorter than A
= 5 u + 1050 - 1 u
= 5 u - 1 u + 1050
= 4 u + 1050
= 4 x 420 + 1050
= 1680 + 1050
= 2730 cm
(b)
Total length of A and C = 5 u + 1050 + 1 u + 210
= 5 u + 1 u + 1050 + 210
= 6 x 420 + 1260 = 2520 + 1260 = 3780 cm Answer(s): (a) 2730 cm; (b) 3780 cm