Question 1179663
<br>
There are an endless number of ways to solve this problem using formal algebra; you have received two responses showing two of those ways.<br>
I would certainly not use the method shown by tutor @Mananth.  She has the strange habit of representing whole numbers using 2 decimal places.<br>
The solution from tutor @MathTherapy is more straightforward.<br>
I would start the way he did but then go a different direction with it.<br>
Subtracting the two equations formed from the given information gives the result that the cost of one shirt and one pair of pants is $37.50:<br>
{{{x+y=37.50}}}<br>
Instead of solving that equation for one variable in terms of the other and finishing the problem using substitution, I would continue with elimination.<br>
Informally, finishing the problem using elimination could go something like this:
one shirt and one pair of pants cost $37.50
so two shirts and two pairs of pants cost 2($37.50)=$75
but three shirts and two pairs of pants cost $85.50, so one shirt costs $85.50-$75=$10.50.
and then one pair of pants costs $37.50-$10.50=$27.<br>
The formal algebra for finishing the problem by that path looks like this:<br>
(1) x+y=$37.50          (from the two original equations)
(2) 2x+2y=2($37.50)=$75    (doubling (1))
(3) 3x+2y=$85.50      (one of the original equations)
(4) x=$85.50-$75=$10.50    (comparing (2) and (3))
(5) y=$37.50-$10.50=$27    (from (1) and (4))<br>