Question 1059710
let x represent the number of t-shits that cost 5 dollars apiece.


let y represent the number of t-shirts that cost 10 dollars apiece.


you bought 5 t-shirts, therefore x + y = 5.


you paid a total of 35 dollars for the t-shirts, therefore 5x + 10y = 35


you have a system of equations that need to be solved simultaneously.


those equations are:


x + y = 5


5x + 10y = 35


from the first equation, you can solve for y to get y = 5 - x.


in the second equation, you can replace y with 5 - x to get 5x + 10 * (5-x) = 35.


simplify this equation to get 5x + 50 - 10x = 35.


combine like terms to get -5x + 50 = 35.


subtract 50 from both sides of the equation to get -5x = -15.


divide both sides of the equation by -5 to get x = 3.


since x + y = 5, then y must be equal to 2.


you bought 3 t-shirts at 5 dollars apiece and 2 t-shirt at 10 dollars apiece.


your total cost is 3 * 5 + 2 * 10 = 15 + 20 = 35.


solution is x = 3 and y = 2.


when you solve the two equations simultaneously, the same solution has to be good for both equations.


x + y = 5 becomes 3 + 2 = 5 so the first equation is satisfied.
5x + 10ty = 35 becomes 15 + 20 = 35 so the second equation is satisfied as well by the same values of x and y.