A piece of ribbon 2600 cm long is cut into 3 parts, C, B and A.
C is 4 times as long as B.
A is 250 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 + 250
Length of C = 4 x (1 u + 250) = 4 u + 1000
Total length of C, B and A
= 4 u + 1000 + 1 u + 250 + 1 u
= 4 u + 1 u + 1 u + 1000 + 250
= 6 u + 1250
6 u + 1250 = 2600
6 u = 2600 - 1250
6 u = 1350
1 u = 1350 ÷ 6 = 225
Length of C longer than B
= 4 u + 1000 - (1 u + 250)
= 4 u - 1 u + 1000 - 250
= 3 u + 750
= 3 x 225 + 750
= 675 + 750
= 1425 cm
(b)
Total length of C and A
= 4 u + 1000 + 1 u
= 5 u + 1000
= 5 x 225 + 1000
= 1125 + 1000
= 2125 cm
Answer(s): (a) 1425 cm; (b) 2125 cm