A piece of ribbon 4900 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 170 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 + 170
Length of B = 3 x (1 u + 170) = 3 u + 510
Total length of B, C and A
= 3 u + 510 + 1 u + 170 + 1 u
= 3 u + 1 u + 1 u + 510 + 170
= 5 u + 680
5 u + 680 = 4900
5 u = 4900 - 680
5 u = 4220
1 u = 4220 ÷ 5 = 844
Length of B longer than C
= 3 u + 510 - (1 u + 170)
= 3 u - 1 u + 510 - 170
= 2 u + 340
= 2 x 844 + 340
= 1688 + 340
= 2028 cm
(b)
Total length of B and A
= 3 u + 510 + 1 u
= 4 u + 510
= 4 x 844 + 510
= 3376 + 510
= 3886 cm
Answer(s): (a) 2028 cm; (b) 3886 cm