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.
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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