A piece of ribbon 3000 cm long is cut into 3 parts, A, B and C.
A is 5 times as long as B.
C is 290 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 + 290
Length of A = 5 x (1 u + 290) = 5 u + 1450
Total length of A, B and C
= 5 u + 1450 + 1 u + 290 + 1 u
= 5 u + 1 u + 1 u + 1450 + 290
= 7 u + 1740
7 u + 1740 = 3000
7 u = 3000 - 1740
7 u = 1260
1 u = 1260 ÷ 7 = 180
Length of A longer than B
= 5 u + 1450 - (1 u + 290)
= 5 u - 1 u + 1450 - 290
= 4 u + 1160
= 4 x 180 + 1160
= 720 + 1160
= 1880 cm
(b)
Total length of A and C
= 5 u + 1450 + 1 u
= 6 u + 1450
= 6 x 180 + 1450
= 1080 + 1450
= 2530 cm
Answer(s): (a) 1880 cm; (b) 2530 cm