A piece of ribbon 2900 cm long is cut into 3 parts, A, B and C.
A is 3 times as long as B.
C is 260 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 + 260
Length of A = 3 x (1 u + 260) = 3 u + 780
Total length of A, B and C
= 3 u + 780 + 1 u + 260 + 1 u
= 3 u + 1 u + 1 u + 780 + 260
= 5 u + 1040
5 u + 1040 = 2900
5 u = 2900 - 1040
5 u = 1860
1 u = 1860 ÷ 5 = 372
Length of C shorter than A
= 3 u + 780 - 1 u
= 3 u - 1 u + 780
= 2 u + 780
= 2 x 372 + 780
= 744 + 780
= 1524 cm
(b)
Total length of A and B = 3 u + 780 + 1 u + 260
= 3 u + 1 u + 780 + 260
= 4 x 372 + 1040 = 1488 + 1040 = 2528 cm Answer(s): (a) 1524 cm; (b) 2528 cm