A piece of ribbon 4000 cm long is cut into 3 parts, B, C and A.
B is 4 times as long as C.
A is 290 cm shorter than C.
Give the answers in cm.
- How much shorter is A than B?
- What is the total length of B and C?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 290
Length of B = 4 x (1 u + 290) = 4 u + 1160
Total length of B, C and A
= 4 u + 1160 + 1 u + 290 + 1 u
= 4 u + 1 u + 1 u + 1160 + 290
= 6 u + 1450
6 u + 1450 = 4000
6 u = 4000 - 1450
6 u = 2550
1 u = 2550 ÷ 6 = 425
Length of A shorter than B
= 4 u + 1160 - 1 u
= 4 u - 1 u + 1160
= 3 u + 1160
= 3 x 425 + 1160
= 1275 + 1160
= 2435 cm
(b)
Total length of B and C = 4 u + 1160 + 1 u + 290
= 4 u + 1 u + 1160 + 290
= 5 x 425 + 1450 = 2125 + 1450 = 3575 cm Answer(s): (a) 2435 cm; (b) 3575 cm