Answer:
$11.7
Step-by-step explanation:
The most important step when solving a word problem is to turn the question into an equation:
[tex]4x+7y=78.3\\3x+5y=57.6[/tex]
Our goal is to solve for x, which represents the price of each Soccer Jerseys.
There are multiple ways to solve a system of equations, I will present 2 methods.
Method 1 | Graphing:
Arguably the easiest way, but only if you have a graphing calculator or somewhere to graph.
Simply graph both equations and the point of intersection of both lines will be the answer for x and y.
The graph should look something like this:
(See picture)
The lines are so close that you can barely see a gap between both lines!
The solution is (11.7, 4.5).
Since we are trying to find x, $11.7 is our answer.
Method 2 | Substitution:
Substitution is in my opinion, the second easiest way to solve a system of equations.
Pick any of the two equations and isolate any of the two variables. Let's isolate the x in the second equation:
[tex]3x+5y=57.6\\3x=57.6-5y\\x=19.2-\frac{5}{3}y[/tex]
After that, we will replace our x value (only in terms of y) into the other equation:
[tex]4x+7y=78.3\\4(19.2-\frac{5}{3}y)+7y=78.3\\76.8-\frac{20}{3}y+7y=78.3\\\frac{1}{3}y=1.5\\y=4.5[/tex]
After finding the value of y, replace it into any of the two equations to find x:
[tex]3x+5y=57.6\\3x+5(4.5)=57.6\\3x+22.5=57.6\\3x=35.1\\x=11.7[/tex]
And we get the same answer as before.
Hope this helps :)
