Question 1014305
a = cost of the skirt.
b = cost of the sweater.
c = cost of the shoes.


a + b + c = 138.


cost of the sweater is 9/8 times the costs of the skirt.


the equation for that is b = 9a/8.


the shoes cost 13 dollars more than the skirt.


the equation for that is c = a + 13


you have 3 equations to work with.


a + b + c = 138
b = 9a/8
c = a + 13


in the equation of a + b + c = 138, replace b with 9a/8 and replace c with a + 13 to get:


a + b + c = 138 becomes a + 9a/8 + a + 13 = 138


combine like terms to get 2a + 9a/8 + 13 = 138.


since 2a = 16a/8, the equation becomes 16a/8 + 9a/8 + 13 = 138


combine like  terms again to get 25a/8 + 13 = 138.


subtract 13 from both sides of this equation to get 25a/8 = 138 - 13.


simplify to get 25a/8 = 125.


multiply both sides of this equation by 8 and divide both sides of this equation by 25 to get a = 8*125/25


this results in a = 40


when a = 40:


9a/8 = 9*40/8 = 9*5 = 45.


a + 13 = 40 + 13 = 53.


a = 40
b = 45
c = 53


a + b + c = 40 + 45 + 53 = 138.
this checks out ok.


b = 9a/8 = 9*40/8 = 45.
this checks out ok.


c = a = 13 = 40 + 13 = 53.
this checks out ok.


the cost per item is:


skirt = 40
sweater = 45
shoes = 53.


that's your solution.