A piece of ribbon 3800 cm long is cut into 3 parts, A, B and C.
A is 5 times as long as B.
C is 260 cm shorter than B.
Give the answers in cm.
- How much longer is A than B?
- What is the total length of A and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 260
Length of A = 5 x (1 u + 260) = 5 u + 1300
Total length of A, B and C
= 5 u + 1300 + 1 u + 260 + 1 u
= 5 u + 1 u + 1 u + 1300 + 260
= 7 u + 1560
7 u + 1560 = 3800
7 u = 3800 - 1560
7 u = 2240
1 u = 2240 ÷ 7 = 320
Length of A longer than B
= 5 u + 1300 - (1 u + 260)
= 5 u - 1 u + 1300 - 260
= 4 u + 1040
= 4 x 320 + 1040
= 1280 + 1040
= 2320 cm
(b)
Total length of A and C
= 5 u + 1300 + 1 u
= 6 u + 1300
= 6 x 320 + 1300
= 1920 + 1300
= 3220 cm
Answer(s): (a) 2320 cm; (b) 3220 cm