You buy 5 small candles and 2 large candles for $15. Your friend buys 6 small candles and 3 large candles for $21.

Small candles cost 1 dollar, large candles cost 5 dollars.

Step-by-step explanation:

Let s represent small candles, L represent large candles.

You: 15 = 5s + 2L

Friend: 21 = 6s + 3L

Now you can solve for s and L, the cost of each candle type!

15 = 5s + 2L Multiply this equation by 3 -> 45 = 15s + 6L

21 = 6s + 3L Multiply this equation by 2 -> 42 = 12s + 6L

Now we have equal L's in both equations. Use elimination to get rid of L! Subtract the equations from each other.

  45 = 15s + 6L

-  42 = 12s + 6L

    3 = 3s + 0L

Now solve for s.

   3 = 3s

    s = 1 dollar

Plug s back in to get L.

15 = 5s + 2L

15 = 5(1) + 2L

15 = 5 + 2L

10 = 2L

L = 5 dollars

so, converting firstly the mixed fractions to improper fractions and then "adding".