Question

three types of shirts sold at a store cost $9,$11, and $12.50. One day the store sells a total of 23 shirts and makes $243 in sales. Twice as many shirts were sold for $12.50 than were sold for $11. Write a system of equations to represent this situation.

Answer 1

The System of equations which represents the situations are;

`z=2y`

`x+y+z=23`

`9x+11y+12.5z=243`

Explanation:

Let the shirt sold at cost $9 be x.

Let the shirt sold at cost $11 be y.

Let the shirt sold at cost $12.50 be z.

Given:

Twice as many shirts were sold for $12.50 than were sold for $11.

Hence it means that shirt sold at at cost $12.50 were 2 times more than shirt sold at cost $11.

Hence framing in equation we get;

`z=2y`

Now Given:

Total Shirts sold = 23

But Total Shirts sold is sum of number of shirt sold at cost $9 and number of shirt sold at cost $11 and number of shirt sold at cost $12.50.

Hence framing in equation we get;

`x+y+z=23`

Also Given:

Total Money made by store = $243

But Total Money made by store is sum of number of shirt sold at cost $9 Multiplied by 9 and number of shirt sold at cost $11 multiplied by 11 and number of shirt sold at cost $12.50 multiplied by 12.50.

Framing in equation form we get;

`9x+11y+12.5z=243`

Hence the System of equations which represents the situations are;

`z=2y`

`x+y+z=23`

`9x+11y+12.5z=243`