A piece of ribbon 2100 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 270 cm shorter than C.
Give the answers in cm.
- How much longer is B than C?
- What is the total length of B and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 270
Length of B = 3 x (1 u + 270) = 3 u + 810
Total length of B, C and A
= 3 u + 810 + 1 u + 270 + 1 u
= 3 u + 1 u + 1 u + 810 + 270
= 5 u + 1080
5 u + 1080 = 2100
5 u = 2100 - 1080
5 u = 1020
1 u = 1020 ÷ 5 = 204
Length of B longer than C
= 3 u + 810 - (1 u + 270)
= 3 u - 1 u + 810 - 270
= 2 u + 540
= 2 x 204 + 540
= 408 + 540
= 948 cm
(b)
Total length of B and A
= 3 u + 810 + 1 u
= 4 u + 810
= 4 x 204 + 810
= 816 + 810
= 1626 cm
Answer(s): (a) 948 cm; (b) 1626 cm