A piece of ribbon 4900 cm long is cut into 3 parts, A, B and C.
A is 5 times as long as B.
C is 210 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 + 210
Length of A = 5 x (1 u + 210) = 5 u + 1050
Total length of A, B and C
= 5 u + 1050 + 1 u + 210 + 1 u
= 5 u + 1 u + 1 u + 1050 + 210
= 7 u + 1260
7 u + 1260 = 4900
7 u = 4900 - 1260
7 u = 3640
1 u = 3640 ÷ 7 = 520
Length of A longer than B
= 5 u + 1050 - (1 u + 210)
= 5 u - 1 u + 1050 - 210
= 4 u + 840
= 4 x 520 + 840
= 2080 + 840
= 2920 cm
(b)
Total length of A and C
= 5 u + 1050 + 1 u
= 6 u + 1050
= 6 x 520 + 1050
= 3120 + 1050
= 4170 cm
Answer(s): (a) 2920 cm; (b) 4170 cm