A piece of ribbon 1300 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 180 cm shorter than C.
Give the answers in cm.
- How much longer is B than C?
- What is the total length of B and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 180
Length of B = 3 x (1 u + 180) = 3 u + 540
Total length of B, C and A
= 3 u + 540 + 1 u + 180 + 1 u
= 3 u + 1 u + 1 u + 540 + 180
= 5 u + 720
5 u + 720 = 1300
5 u = 1300 - 720
5 u = 580
1 u = 580 ÷ 5 = 116
Length of B longer than C
= 3 u + 540 - (1 u + 180)
= 3 u - 1 u + 540 - 180
= 2 u + 360
= 2 x 116 + 360
= 232 + 360
= 592 cm
(b)
Total length of B and A
= 3 u + 540 + 1 u
= 4 u + 540
= 4 x 116 + 540
= 464 + 540
= 1004 cm
Answer(s): (a) 592 cm; (b) 1004 cm