Three types of shirts sold at a store cost $9.00, $11.00, and $12.50. One day, the store sells a total of 23 shirts and makes $243 on the sales. Twice as many shirts were sold for $12.50 than were sold for $11.00. If x represents $9.00 shirts, y represents $11.00 shirts and z represents $12.50 shirts, how many of each type of shirt were sold?
x = number of 9 dollar shirts. y = number of 11 dollar shirts. z = number of 12.50 dollar shirts.
x + y + z = 23. 9x +11y +12.5z=243.
z = 2y.
We can replace the z with 2y. Our new equation becomes 9x +11y +12.5(2y)=243. Which becomes 9x + 11y + 25y. Which finally becomes 9x + 36y = 243. Now we can just use smart guess and check. If y = 1, x has to become 23. This doesn't work because it has to add up to 23. It will add up to 26. x+3y has to equal 23. If y = 3, x = 9. That is too little. So we try y = 2, x = 19. This is still too much. So...there is no solution to this problem. Unless I did something wrong.