A piece of ribbon 3500 cm long is cut into 3 parts, A, C and B.
A is 3 times as long as C.
B is 130 cm shorter than C.
Give the answers in cm.
- How much longer is A than C?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of B = 1 u
Length of C = 1 u + 130
Length of A = 3 x (1 u + 130) = 3 u + 390
Total length of A, C and B
= 3 u + 390 + 1 u + 130 + 1 u
= 3 u + 1 u + 1 u + 390 + 130
= 5 u + 520
5 u + 520 = 3500
5 u = 3500 - 520
5 u = 2980
1 u = 2980 ÷ 5 = 596
Length of A longer than C
= 3 u + 390 - (1 u + 130)
= 3 u - 1 u + 390 - 130
= 2 u + 260
= 2 x 596 + 260
= 1192 + 260
= 1452 cm
(b)
Total length of A and B
= 3 u + 390 + 1 u
= 4 u + 390
= 4 x 596 + 390
= 2384 + 390
= 2774 cm
Answer(s): (a) 1452 cm; (b) 2774 cm