Question

One hat company makes and sells two types of hats. The Bradley hat requires 4 yards of leather. The karli hat requires 6 yards of leather. If the company used 100 yards of leather to make 19 hats, how many of each type did the company make

Answer 1

The Company made 6 Bradley hats and 12 Karli hats.

Explanation:

Given,

Total Amount of leather = 100 yards

Total number of hats = 19

Solution,

Let the number of Bradley hat be x.

And also let the number of Karli hat be y.

Total number of hats = 19

`\therefore x+y=19\ \ \ \ \ equation\ 1`

Now, Bradly hats requires 4 yards and Karli hats requires 6 yards of leather.

So framing the above sentence in equation form, we get;

`4x+6y=100\ \ \ \ \ equation\ 2`

Now, multiplying equation 1 by 4, we get;

`4(x+y)=19*4\\\\4x+4y=76\ \ \ \ \ equation\ 3`

Now we subtract equation 3 from equation 2, we get;

`(4x+6y)-(4x+6y)=100-76\\\\4x+6y-4x-4y=24\\\\2y=24\\\\y=(24)/(2)=12`

`y=12`

On substituting the value of y in equation 1, we get the value of x.

`x+y=19\\\\x+12=19\\\\x=19-12=6`

Hence The Company made 6 Bradley hats and 12 Karli hats.