A piece of ribbon 3200 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 130 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 + 130
Length of A = 3 x (1 u + 130) = 3 u + 390
Total length of A, B and C
= 3 u + 390 + 1 u + 130 + 1 u
= 3 u + 1 u + 1 u + 390 + 130
= 5 u + 520
5 u + 520 = 3200
5 u = 3200 - 520
5 u = 2680
1 u = 2680 ÷ 5 = 536
Length of C shorter than A
= 3 u + 390 - 1 u
= 3 u - 1 u + 390
= 2 u + 390
= 2 x 536 + 390
= 1072 + 390
= 1462 cm
(b)
Total length of A and B = 3 u + 390 + 1 u + 130
= 3 u + 1 u + 390 + 130
= 4 x 536 + 520 = 2144 + 520 = 2664 cm Answer(s): (a) 1462 cm; (b) 2664 cm