A piece of ribbon 1800 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 270 cm shorter than B.
Give the answers in cm.
- How much longer is C than B?
- What is the total length of C and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 270
Length of C = 3 x (1 u + 270) = 3 u + 810
Total length of C, B and A
= 3 u + 810 + 1 u + 270 + 1 u
= 3 u + 1 u + 1 u + 810 + 270
= 5 u + 1080
5 u + 1080 = 1800
5 u = 1800 - 1080
5 u = 720
1 u = 720 ÷ 5 = 144
Length of C longer than B
= 3 u + 810 - (1 u + 270)
= 3 u - 1 u + 810 - 270
= 2 u + 540
= 2 x 144 + 540
= 288 + 540
= 828 cm
(b)
Total length of C and A
= 3 u + 810 + 1 u
= 4 u + 810
= 4 x 144 + 810
= 576 + 810
= 1386 cm
Answer(s): (a) 828 cm; (b) 1386 cm