A piece of ribbon 1900 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 270 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 + 270
Length of A = 3 x (1 u + 270) = 3 u + 810
Total length of A, B and C
= 3 u + 810 + 1 u + 270 + 1 u
= 3 u + 1 u + 1 u + 810 + 270
= 5 u + 1080
5 u + 1080 = 1900
5 u = 1900 - 1080
5 u = 820
1 u = 820 ÷ 5 = 164
Length of A longer than B
= 3 u + 810 - (1 u + 270)
= 3 u - 1 u + 810 - 270
= 2 u + 540
= 2 x 164 + 540
= 328 + 540
= 868 cm
(b)
Total length of A and C
= 3 u + 810 + 1 u
= 4 u + 810
= 4 x 164 + 810
= 656 + 810
= 1466 cm
Answer(s): (a) 868 cm; (b) 1466 cm