A piece of ribbon 1900 cm long is cut into 3 parts, C, A and B.
C is 3 times as long as A.
B is 160 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 + 160
Length of C = 3 x (1 u + 160) = 3 u + 480
Total length of C, A and B
= 3 u + 480 + 1 u + 160 + 1 u
= 3 u + 1 u + 1 u + 480 + 160
= 5 u + 640
5 u + 640 = 1900
5 u = 1900 - 640
5 u = 1260
1 u = 1260 ÷ 5 = 252
Length of C longer than A
= 3 u + 480 - (1 u + 160)
= 3 u - 1 u + 480 - 160
= 2 u + 320
= 2 x 252 + 320
= 504 + 320
= 824 cm
(b)
Total length of C and B
= 3 u + 480 + 1 u
= 4 u + 480
= 4 x 252 + 480
= 1008 + 480
= 1488 cm
Answer(s): (a) 824 cm; (b) 1488 cm