A piece of ribbon 2300 cm long is cut into 3 parts, C, A and B.
C is 5 times as long as A.
B is 290 cm shorter than A.
Give the answers in cm.
- How much longer is C than A?
- What is the total length of C and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of A = 1 u + 290
Length of C = 5 x (1 u + 290) = 5 u + 1450
Total length of C, A and B
= 5 u + 1450 + 1 u + 290 + 1 u
= 5 u + 1 u + 1 u + 1450 + 290
= 7 u + 1740
7 u + 1740 = 2300
7 u = 2300 - 1740
7 u = 560
1 u = 560 ÷ 7 = 80
Length of C longer than A
= 5 u + 1450 - (1 u + 290)
= 5 u - 1 u + 1450 - 290
= 4 u + 1160
= 4 x 80 + 1160
= 320 + 1160
= 1480 cm
(b)
Total length of C and B
= 5 u + 1450 + 1 u
= 6 u + 1450
= 6 x 80 + 1450
= 480 + 1450
= 1930 cm
Answer(s): (a) 1480 cm; (b) 1930 cm