A piece of ribbon 1700 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 290 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 + 290
Length of A = 3 x (1 u + 290) = 3 u + 870
Total length of A, B and C
= 3 u + 870 + 1 u + 290 + 1 u
= 3 u + 1 u + 1 u + 870 + 290
= 5 u + 1160
5 u + 1160 = 1700
5 u = 1700 - 1160
5 u = 540
1 u = 540 ÷ 5 = 108
Length of A longer than B
= 3 u + 870 - (1 u + 290)
= 3 u - 1 u + 870 - 290
= 2 u + 580
= 2 x 108 + 580
= 216 + 580
= 796 cm
(b)
Total length of A and C
= 3 u + 870 + 1 u
= 4 u + 870
= 4 x 108 + 870
= 432 + 870
= 1302 cm
Answer(s): (a) 796 cm; (b) 1302 cm