A piece of ribbon 4600 cm long is cut into 3 parts, C, B and A.
C is 3 times as long as B.
A is 190 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 + 190
Length of C = 3 x (1 u + 190) = 3 u + 570
Total length of C, B and A
= 3 u + 570 + 1 u + 190 + 1 u
= 3 u + 1 u + 1 u + 570 + 190
= 5 u + 760
5 u + 760 = 4600
5 u = 4600 - 760
5 u = 3840
1 u = 3840 ÷ 5 = 768
Length of A shorter than C
= 3 u + 570 - 1 u
= 3 u - 1 u + 570
= 2 u + 570
= 2 x 768 + 570
= 1536 + 570
= 2106 cm
(b)
Total length of C and B = 3 u + 570 + 1 u + 190
= 3 u + 1 u + 570 + 190
= 4 x 768 + 760 = 3072 + 760 = 3832 cm Answer(s): (a) 2106 cm; (b) 3832 cm