A piece of ribbon 1900 cm long is cut into 3 parts, C, A and B.
C is 4 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 = 4 x (1 u + 290) = 4 u + 1160
Total length of C, A and B
= 4 u + 1160 + 1 u + 290 + 1 u
= 4 u + 1 u + 1 u + 1160 + 290
= 6 u + 1450
6 u + 1450 = 1900
6 u = 1900 - 1450
6 u = 450
1 u = 450 ÷ 6 = 75
Length of C longer than A
= 4 u + 1160 - (1 u + 290)
= 4 u - 1 u + 1160 - 290
= 3 u + 870
= 3 x 75 + 870
= 225 + 870
= 1095 cm
(b)
Total length of C and B
= 4 u + 1160 + 1 u
= 5 u + 1160
= 5 x 75 + 1160
= 375 + 1160
= 1535 cm
Answer(s): (a) 1095 cm; (b) 1535 cm