A piece of ribbon 1200 cm long is cut into 3 parts, A, B and C.
A is 3 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 = 3 x (1 u + 260) = 3 u + 780
Total length of A, B and C
= 3 u + 780 + 1 u + 260 + 1 u
= 3 u + 1 u + 1 u + 780 + 260
= 5 u + 1040
5 u + 1040 = 1200
5 u = 1200 - 1040
5 u = 160
1 u = 160 ÷ 5 = 32
Length of A longer than B
= 3 u + 780 - (1 u + 260)
= 3 u - 1 u + 780 - 260
= 2 u + 520
= 2 x 32 + 520
= 64 + 520
= 584 cm
(b)
Total length of A and C
= 3 u + 780 + 1 u
= 4 u + 780
= 4 x 32 + 780
= 128 + 780
= 908 cm
Answer(s): (a) 584 cm; (b) 908 cm