Question

a long wire of some length is cut into small pieces of 216 cm,leaves a small piece of length of 89 cm .if this part were cut into equal pieces each of 18 cm,the length of the leftover wire would be :

Answer 1

[tex]\text{Let the number of 216cm pieces be }x.\\ \\\text{Then, total length of the wire}=(216x+89) cm[/tex]

[tex]\text{The wire is cut into equal pieces each of 18cm.}\\ \\ \text{Then, number of pieces}\\ \\= \frac{\text{total length of the wire}}{\text{length of each piece}}\\ \\= \frac{216x+89}{18}\\ \\= \frac{216x}{18}+ \frac{89}{18}\\\\=12x+4 \frac{17}{18} [/tex]

[tex]\text{The fractional part } \frac{17}{18} \text{ represents the left over part.}\\ \\ \text{Numerator 17 is the remainder when 89 is divided by 18.}\\ \\ [/tex]

[tex]\text{Therefore, the length of the left over part is 17 cm} \\ \\ \text{Answer: The length of the left over part is 17 cm }[/tex]

Answer 2

Solution :-

The length of the remaining part of wire after cutting the long wire into pieces each of 216 cm = 89 cm

The leftover part of 89 cm is cut into equal pieces each of 18 cm

Total pieces of 18 cm each = 89/18 = 4 pieces (Leaving a remainder of 17)

Total pieces of length 18 cm can be cut out of 89 cm = 4

Length of the left over part = 
89 - (18*4) 
89 - 72
17 cm

So, the length of leftover wire is 17 cm

Answer