A piece of ribbon 5000 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 260 cm shorter than B.
Give the answers in cm.
- How much shorter is A than C?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of B = 1 u + 260
Length of C = 3 x (1 u + 260) = 3 u + 780
Total length of C, B and A
= 3 u + 780 + 1 u + 260 + 1 u
= 3 u + 1 u + 1 u + 780 + 260
= 5 u + 1040
5 u + 1040 = 5000
5 u = 5000 - 1040
5 u = 3960
1 u = 3960 ÷ 5 = 792
Length of A shorter than C
= 3 u + 780 - 1 u
= 3 u - 1 u + 780
= 2 u + 780
= 2 x 792 + 780
= 1584 + 780
= 2364 cm
(b)
Total length of C and B = 3 u + 780 + 1 u + 260
= 3 u + 1 u + 780 + 260
= 4 x 792 + 1040 = 3168 + 1040 = 4208 cm Answer(s): (a) 2364 cm; (b) 4208 cm