Problem solving with two and three variables

Question

Mary works part time selling both hats and scarves. One week she earns $114.00 by selling 8 hats and 10 scarves. The following week she sold 12 hats and 6 scarves, and earned $108.00. How much does she earn for each hat and for each scarf she sells?

Answer 1

I'll just work this one problem and hope that you can discern a pattern or similar approach for the other two problems that you submitted.

 

Let H = selling price of one hat & let S = selling price of one scarf.  ⇐This is the key step!

 

8H + 10S = 114

12H + 6S = 108

 

That's a system of two equations (linear) in two unknowns, and you can solve it by any of the ways that you have learned in Algebra, fairly easily.  Just remember to check your answers.