10. At a sale on candles, Lexi bought two large candles and five small candles and paid $30. Carl bought one large candle and three small candles and paid $16.75. Find the cost of each

Large candle) $6.25

Small candle) $3.5

Step-by-step explanation:

Let x be the cost of a large candle and y be the cost of a small candle.

Because Lexi bought two large candles and five small candles for $30, the first equation is 2x+5y=30.

Because Carl bought one large candle and three small candles for $16.75, the second equation is x+3y=16.75

We have two equations:

2x+5y=30 and x+3y=16.75

   1) Multiply both sides of x+3y=16.75 by 2 to get 2x+6y=33.5

   2) Subract the two equations

       2x+6y=33.5

      - 2x+5y=30

      =        y=3.5

   3) Plug y=3.5 into one of the equations.

       2x+5(3.5)=30

       2x+17.5=30

       2x=12.5

         x=6.25

   4) Check the work by plugging both variable in the other equation

        6.25+3(3.5)=16.75

        6.25+10.5=16.75

        6.75=16.75

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