A piece of ribbon 4900 cm long is cut into 3 parts, A, B and C.
A is 4 times as long as B.
C is 260 cm shorter than B.
Give the answers in cm.
- How much shorter is C than A?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 260
Length of A = 4 x (1 u + 260) = 4 u + 1040
Total length of A, B and C
= 4 u + 1040 + 1 u + 260 + 1 u
= 4 u + 1 u + 1 u + 1040 + 260
= 6 u + 1300
6 u + 1300 = 4900
6 u = 4900 - 1300
6 u = 3600
1 u = 3600 ÷ 6 = 600
Length of C shorter than A
= 4 u + 1040 - 1 u
= 4 u - 1 u + 1040
= 3 u + 1040
= 3 x 600 + 1040
= 1800 + 1040
= 2840 cm
(b)
Total length of A and B = 4 u + 1040 + 1 u + 260
= 4 u + 1 u + 1040 + 260
= 5 x 600 + 1300 = 3000 + 1300 = 4300 cm Answer(s): (a) 2840 cm; (b) 4300 cm