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 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 = 3 x (1 u + 210) = 3 u + 630
Total length of A, B and C
= 3 u + 630 + 1 u + 210 + 1 u
= 3 u + 1 u + 1 u + 630 + 210
= 5 u + 840
5 u + 840 = 1900
5 u = 1900 - 840
5 u = 1060
1 u = 1060 ÷ 5 = 212
Length of A longer than B
= 3 u + 630 - (1 u + 210)
= 3 u - 1 u + 630 - 210
= 2 u + 420
= 2 x 212 + 420
= 424 + 420
= 844 cm
(b)
Total length of A and C
= 3 u + 630 + 1 u
= 4 u + 630
= 4 x 212 + 630
= 848 + 630
= 1478 cm
Answer(s): (a) 844 cm; (b) 1478 cm