A shirt boutique purchased 100 new shirts for $1072. The short-sleeved shirts cost $10 each and the long-sleeved shirts cost $12 each. How many short-sleeved shirts were purchased?

one equation would be S+ L=36for the number of shirts sold.

64 short-sleeved shirts were purchased.

Step-by-step explanation: (x = short-sleeved shirts. y = long-sleeved shirts.)  

x + y = 100

10x + 12y = 1072

—12(x + y = 100) >>> -12x - 12y = -1200                                                                                                           10x + 12y = 1072 (add the equations and cancel out the 12y)

-2x/-2 (-2 cancels out) = -128/-2   (divide both by -2)

x = 64 shirts purchased for $10 each.   (Hope this helped!)

(vvvThis next part doesn’t answer the question, but I should finish the equation.)

(Plug in 64 for x)>>> 64 + y = 100 (then, subtract 64 from both sides) >>> 64 - 64 = 0 (they cancel out) and 100 - 64 = 36

y = 36 shirts purchased for $12 each.

I really hope this helped! :)

yes. we do proportions in probabilities.