A piece of ribbon 3800 cm long is cut into 3 parts, A, B and C.
A is 2 times as long as B.
C is 260 cm shorter than B.
Give the answers in cm.
- How much longer is A than B?
- What is the total length of A and C?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 260
Length of A = 2 x (1 u + 260) = 2 u + 520
Total length of A, B and C
= 2 u + 520 + 1 u + 260 + 1 u
= 2 u + 1 u + 1 u + 520 + 260
= 4 u + 780
4 u + 780 = 3800
4 u = 3800 - 780
4 u = 3020
1 u = 3020 ÷ 4 = 755
Length of A longer than B
= 2 u + 520 - (1 u + 260)
= 2 u - 1 u + 520 - 260
= 1 u + 260
= 1 x 755 + 260
= 755 + 260
= 1015 cm
(b)
Total length of A and C
= 2 u + 520 + 1 u
= 3 u + 520
= 3 x 755 + 520
= 2265 + 520
= 2785 cm
Answer(s): (a) 1015 cm; (b) 2785 cm