A piece of ribbon 1400 cm long is cut into 3 parts, C, B and A.
C is 5 times as long as B.
A is 280 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 + 280
Length of C = 5 x (1 u + 280) = 5 u + 1400
Total length of C, B and A
= 5 u + 1400 + 1 u + 280 + 1 u
= 5 u + 1 u + 1 u + 1400 + 280
= 7 u + 1680
7 u + 1680 = 1400
7 u = 1400 - 1680
7 u = -280
1 u = -280 ÷ 7 = -40
Length of C longer than B
= 5 u + 1400 - (1 u + 280)
= 5 u - 1 u + 1400 - 280
= 4 u + 1120
= 4 x -40 + 1120
= -160 + 1120
= 960 cm
(b)
Total length of C and A
= 5 u + 1400 + 1 u
= 6 u + 1400
= 6 x -40 + 1400
= -240 + 1400
= 1160 cm
Answer(s): (a) 960 cm; (b) 1160 cm