A piece of ribbon 4200 cm long is cut into 3 parts, C, A and B.
C is 4 times as long as A.
B is 210 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 + 210
Length of C = 4 x (1 u + 210) = 4 u + 840
Total length of C, A and B
= 4 u + 840 + 1 u + 210 + 1 u
= 4 u + 1 u + 1 u + 840 + 210
= 6 u + 1050
6 u + 1050 = 4200
6 u = 4200 - 1050
6 u = 3150
1 u = 3150 ÷ 6 = 525
Length of C longer than A
= 4 u + 840 - (1 u + 210)
= 4 u - 1 u + 840 - 210
= 3 u + 630
= 3 x 525 + 630
= 1575 + 630
= 2205 cm
(b)
Total length of C and B
= 4 u + 840 + 1 u
= 5 u + 840
= 5 x 525 + 840
= 2625 + 840
= 3465 cm
Answer(s): (a) 2205 cm; (b) 3465 cm