Question

William is setting up for folding chairs for a meeting he arranges the chairs and seven rows of the same link he has three chairs left over if he arranges the chairs in five rows the same length he has 21 left over how many chairs does he have left

Answer 1

Answer:

William has a total of 66 chairs.

Step-by-step explanation:

Let the number of chairs in each row be 'x'.

Also let the Total number of chairs be 'y'.

Given:

If he arranges the chairs in seven rows of the same length he has three chairs left

Number of rows = 7

Number of chairs left = 3

Now we can say that;

Total number of chairs will be equal to number of chairs in each row multiplied by Number of rows plus Number of chairs left.

framing in equation form we get;

$y=7x+3$

Also Given:

If he arranges the chairs in five rows of the same length he has 21 chairs left

Number of rows = 5

Number of chairs left = 21

Now we can say that;

Total number of chairs will be equal to number of chairs in each row multiplied by Number of rows plus Number of chairs left.

framing in equation form we get;

$y=5x+21$

Now we know that Total number of chairs are same.

Hence we can say that both the equations are equal.

$7x+3=5x+21$

Combining like terms we get;

$7x-5x=21-3\\\\2x= 18$

Dividing both side by 2 we get;

$\frac{2x}{2}=\frac{18}{2}\\\\x=9$

So we can that there are 9 chairs in each row.

Now to find the total number of chairs he has we will substitute value of x in any of the equation we get;

$y =7x+3\\\\y=7\times9+3\\\\y=63+3 =66$

Hence William has a total of 66 chairs.