A piece of ribbon 1700 cm long is cut into 3 parts, B, A and C.
B is 4 times as long as A.
C is 280 cm shorter than A.
Give the answers in cm.
- How much longer is B than A?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of A = 1 u + 280
Length of B = 4 x (1 u + 280) = 4 u + 1120
Total length of B, A and C
= 4 u + 1120 + 1 u + 280 + 1 u
= 4 u + 1 u + 1 u + 1120 + 280
= 6 u + 1400
6 u + 1400 = 1700
6 u = 1700 - 1400
6 u = 300
1 u = 300 ÷ 6 = 50
Length of B longer than A
= 4 u + 1120 - (1 u + 280)
= 4 u - 1 u + 1120 - 280
= 3 u + 840
= 3 x 50 + 840
= 150 + 840
= 990 cm
(b)
Total length of B and C
= 4 u + 1120 + 1 u
= 5 u + 1120
= 5 x 50 + 1120
= 250 + 1120
= 1370 cm
Answer(s): (a) 990 cm; (b) 1370 cm