A piece of ribbon 1100 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 210 cm shorter than C.
Give the answers in cm.
- How much longer is A than C?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of C = 1 u + 210
Length of A = 3 x (1 u + 210) = 3 u + 630
Total length of A, C and B
= 3 u + 630 + 1 u + 210 + 1 u
= 3 u + 1 u + 1 u + 630 + 210
= 5 u + 840
5 u + 840 = 1100
5 u = 1100 - 840
5 u = 260
1 u = 260 ÷ 5 = 52
Length of A longer than C
= 3 u + 630 - (1 u + 210)
= 3 u - 1 u + 630 - 210
= 2 u + 420
= 2 x 52 + 420
= 104 + 420
= 524 cm
(b)
Total length of A and B
= 3 u + 630 + 1 u
= 4 u + 630
= 4 x 52 + 630
= 208 + 630
= 838 cm
Answer(s): (a) 524 cm; (b) 838 cm