A piece of ribbon 4400 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 170 cm shorter than B.
Give the answers in cm.
- How much shorter is C than A?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 170
Length of A = 3 x (1 u + 170) = 3 u + 510
Total length of A, B and C
= 3 u + 510 + 1 u + 170 + 1 u
= 3 u + 1 u + 1 u + 510 + 170
= 5 u + 680
5 u + 680 = 4400
5 u = 4400 - 680
5 u = 3720
1 u = 3720 ÷ 5 = 744
Length of C shorter than A
= 3 u + 510 - 1 u
= 3 u - 1 u + 510
= 2 u + 510
= 2 x 744 + 510
= 1488 + 510
= 1998 cm
(b)
Total length of A and B = 3 u + 510 + 1 u + 170
= 3 u + 1 u + 510 + 170
= 4 x 744 + 680 = 2976 + 680 = 3656 cm Answer(s): (a) 1998 cm; (b) 3656 cm