Let the cost of a shirt and pair of pants be S, and P, respectively

Then we get: 3S + 2P = 85.5 ------ eq (i)

Also, 4S + 3P = 123 ------ eq (ii)

Subtract eq (i) from eq (ii) to get: S + P = 37.5, or S = 37.5 - P

Substitute the value of S into eq (i) to get an equation in P. 

From there, solve for P to get a pair of pants, or  

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


There are an endless number of ways to solve this problem using formal algebra; you have received two responses showing two of those ways.


I would certainly not use the method shown by tutor @Mananth.  She has the strange habit of representing whole numbers using 2 decimal places.


The solution from tutor @MathTherapy is more straightforward.


I would start the way he did but then go a different direction with it.


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:





Instead of solving that equation for one variable in terms of the other and finishing the problem using substitution, I would continue with elimination.


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.


The formal algebra for finishing the problem by that path looks like this:


(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))


 

RELATED QUESTIONS

At the same store, Leigh bought 2 pairs of pants and 5 shirts for $61, and Jessica bought  (answered by addingup)

Shopping at Super Sale Days, Martha buys her children 3 shirts and 2 pairs of pants for... (answered by FrankM)

8 shirts and 5 pairs of pants cost $695 altogether. 3 shirts and three pairs of pants... (answered by stanbon)

Carla, Beth, and Heidi went on a shopping spree to get ready for college.  Carla bought 3  (answered by TimothyLamb)

Billy went to the store and bought 5 pants and 3 shirts for $145. He went again the... (answered by addingup,Alan3354)

mr. salazar bought 3 shirts and 2 pants for php.2150. a month later , at the same price,... (answered by mananth)

Esther bought three shirts for a total of $32 and 3 equally priced pairs of pants. She... (answered by unlockmath)

For a trip a traveler packed 4 pairs of pants, 7 shirts, and 3 pairs of shoes. How many... (answered by richwmiller)

If Rolly has 2 T-shirts, 6 pairs of pants, and 3 pairs of shoes, how many possibilities... (answered by ikleyn)