A piece of ribbon 2600 cm long is cut into 3 parts, B, A and C.
B is 3 times as long as A.
C is 250 cm shorter than A.
Give the answers in cm.
- How much shorter is C than B?
- What is the total length of B and A?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of A = 1 u + 250
Length of B = 3 x (1 u + 250) = 3 u + 750
Total length of B, A and C
= 3 u + 750 + 1 u + 250 + 1 u
= 3 u + 1 u + 1 u + 750 + 250
= 5 u + 1000
5 u + 1000 = 2600
5 u = 2600 - 1000
5 u = 1600
1 u = 1600 ÷ 5 = 320
Length of C shorter than B
= 3 u + 750 - 1 u
= 3 u - 1 u + 750
= 2 u + 750
= 2 x 320 + 750
= 640 + 750
= 1390 cm
(b)
Total length of B and A = 3 u + 750 + 1 u + 250
= 3 u + 1 u + 750 + 250
= 4 x 320 + 1000 = 1280 + 1000 = 2280 cm Answer(s): (a) 1390 cm; (b) 2280 cm