A piece of ribbon 4200 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 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 + 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 = 4200
5 u = 4200 - 760
5 u = 3440
1 u = 3440 ÷ 5 = 688
Length of C longer than B
= 3 u + 570 - (1 u + 190)
= 3 u - 1 u + 570 - 190
= 2 u + 380
= 2 x 688 + 380
= 1376 + 380
= 1756 cm
(b)
Total length of C and A
= 3 u + 570 + 1 u
= 4 u + 570
= 4 x 688 + 570
= 2752 + 570
= 3322 cm
Answer(s): (a) 1756 cm; (b) 3322 cm