A piece of ribbon 1500 cm long is cut into 3 parts, A, C and B.
A is 4 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 = 4 x (1 u + 210) = 4 u + 840
Total length of A, C and B
= 4 u + 840 + 1 u + 210 + 1 u
= 4 u + 1 u + 1 u + 840 + 210
= 6 u + 1050
6 u + 1050 = 1500
6 u = 1500 - 1050
6 u = 450
1 u = 450 ÷ 6 = 75
Length of A longer than C
= 4 u + 840 - (1 u + 210)
= 4 u - 1 u + 840 - 210
= 3 u + 630
= 3 x 75 + 630
= 225 + 630
= 855 cm
(b)
Total length of A and B
= 4 u + 840 + 1 u
= 5 u + 840
= 5 x 75 + 840
= 375 + 840
= 1215 cm
Answer(s): (a) 855 cm; (b) 1215 cm