A piece of ribbon 2200 cm long is cut into 3 parts, B, C and A.
B is 3 times as long as C.
A is 190 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 + 190
Length of B = 3 x (1 u + 190) = 3 u + 570
Total length of B, C and A
= 3 u + 570 + 1 u + 190 + 1 u
= 3 u + 1 u + 1 u + 570 + 190
= 5 u + 760
5 u + 760 = 2200
5 u = 2200 - 760
5 u = 1440
1 u = 1440 ÷ 5 = 288
Length of B longer than C
= 3 u + 570 - (1 u + 190)
= 3 u - 1 u + 570 - 190
= 2 u + 380
= 2 x 288 + 380
= 576 + 380
= 956 cm
(b)
Total length of B and A
= 3 u + 570 + 1 u
= 4 u + 570
= 4 x 288 + 570
= 1152 + 570
= 1722 cm
Answer(s): (a) 956 cm; (b) 1722 cm