A piece of ribbon 2400 cm long is cut into 3 parts, C, A and B.
C is 3 times as long as A.
B is 260 cm shorter than A.
Give the answers in cm.
- How much longer is C than A?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 260
Length of C = 3 x (1 u + 260) = 3 u + 780
Total length of C, A and B
= 3 u + 780 + 1 u + 260 + 1 u
= 3 u + 1 u + 1 u + 780 + 260
= 5 u + 1040
5 u + 1040 = 2400
5 u = 2400 - 1040
5 u = 1360
1 u = 1360 ÷ 5 = 272
Length of C longer than A
= 3 u + 780 - (1 u + 260)
= 3 u - 1 u + 780 - 260
= 2 u + 520
= 2 x 272 + 520
= 544 + 520
= 1064 cm
(b)
Total length of C and B
= 3 u + 780 + 1 u
= 4 u + 780
= 4 x 272 + 780
= 1088 + 780
= 1868 cm
Answer(s): (a) 1064 cm; (b) 1868 cm