SOLUTION: Wil paid $35 for 5 T-shirts. Some of the T-shirts cost $5 each and the rest cost $10 each. Write and solve a system of equations to represent this situation. Interpret the solution

Question 1059710: Wil paid $35 for 5 T-shirts. Some of the T-shirts cost $5 each and the rest cost $10 each. Write and solve a system of equations to represent this situation. Interpret the solution.
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
You can account for how many T-shirts;
you can account for the total cost of the T-shirts;
Those are your two linear equations in two unknown variables, forming the system of equations. You must pick a variable for how many of the $5 shirts and another variable for how many of the $10 shirts.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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