A piece of ribbon 1900 cm long is cut into 3 parts, C, A and B.
C is 3 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 = 3 x (1 u + 290) = 3 u + 870
Total length of C, A and B
= 3 u + 870 + 1 u + 290 + 1 u
= 3 u + 1 u + 1 u + 870 + 290
= 5 u + 1160
5 u + 1160 = 1900
5 u = 1900 - 1160
5 u = 740
1 u = 740 ÷ 5 = 148
Length of C longer than A
= 3 u + 870 - (1 u + 290)
= 3 u - 1 u + 870 - 290
= 2 u + 580
= 2 x 148 + 580
= 296 + 580
= 876 cm
(b)
Total length of C and B
= 3 u + 870 + 1 u
= 4 u + 870
= 4 x 148 + 870
= 592 + 870
= 1462 cm
Answer(s): (a) 876 cm; (b) 1462 cm