A piece of ribbon 1200 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 190 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 + 190
Length of A = 3 x (1 u + 190) = 3 u + 570
Total length of A, C and B
= 3 u + 570 + 1 u + 190 + 1 u
= 3 u + 1 u + 1 u + 570 + 190
= 5 u + 760
5 u + 760 = 1200
5 u = 1200 - 760
5 u = 440
1 u = 440 ÷ 5 = 88
Length of B shorter than A
= 3 u + 570 - 1 u
= 3 u - 1 u + 570
= 2 u + 570
= 2 x 88 + 570
= 176 + 570
= 746 cm
(b)
Total length of A and C = 3 u + 570 + 1 u + 190
= 3 u + 1 u + 570 + 190
= 4 x 88 + 760 = 352 + 760 = 1112 cm Answer(s): (a) 746 cm; (b) 1112 cm