A piece of ribbon 2800 cm long is cut into 3 parts, A, B and C.
A is 4 times as long as B.
C is 170 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 + 170
Length of A = 4 x (1 u + 170) = 4 u + 680
Total length of A, B and C
= 4 u + 680 + 1 u + 170 + 1 u
= 4 u + 1 u + 1 u + 680 + 170
= 6 u + 850
6 u + 850 = 2800
6 u = 2800 - 850
6 u = 1950
1 u = 1950 ÷ 6 = 325
Length of A longer than B
= 4 u + 680 - (1 u + 170)
= 4 u - 1 u + 680 - 170
= 3 u + 510
= 3 x 325 + 510
= 975 + 510
= 1485 cm
(b)
Total length of A and C
= 4 u + 680 + 1 u
= 5 u + 680
= 5 x 325 + 680
= 1625 + 680
= 2305 cm
Answer(s): (a) 1485 cm; (b) 2305 cm