A piece of ribbon 3500 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 160 cm shorter than C.
Give the answers in cm.
- How much longer is B than C?
- What is the total length of B and A?
(a)
Choose the shortest length to be 1 u.
Length of A = 1 u
Length of C = 1 u + 160
Length of B = 3 x (1 u + 160) = 3 u + 480
Total length of B, C and A
= 3 u + 480 + 1 u + 160 + 1 u
= 3 u + 1 u + 1 u + 480 + 160
= 5 u + 640
5 u + 640 = 3500
5 u = 3500 - 640
5 u = 2860
1 u = 2860 ÷ 5 = 572
Length of B longer than C
= 3 u + 480 - (1 u + 160)
= 3 u - 1 u + 480 - 160
= 2 u + 320
= 2 x 572 + 320
= 1144 + 320
= 1464 cm
(b)
Total length of B and A
= 3 u + 480 + 1 u
= 4 u + 480
= 4 x 572 + 480
= 2288 + 480
= 2768 cm
Answer(s): (a) 1464 cm; (b) 2768 cm