Problem No. 24 in section 1.7. is a mixture problem I cannot make out the equati

Question

Problem No. 24 in section 1.7. is a mixture problem I cannot make out the equation to get reasonable numbersthat I think are correct. One of my attemted equations is $.25X+$.45(30-x)=$12.50(30). I thought this would figure the original quantity of each candy. I come up with -1807.5 for x that cannot be correct i aslo tried everything the same but after the= put $12.50/30. I also dont know if they are asking for $12.50 plus $3.00 or just $3.00. Can someone please help me get rolling by answering these questions?
The problem reads like this..A candy store sells boxes of candy containing caramels and cremes. Eadc box sells for $12.50 and holds 30 pieces of candy(all pieces are the same size). If the caramels cost $.25 and the cremes $.45 to produce, how many of each should be in a box to make a profit of $3.00.

Explanation / Answer

For your questions, you were on the right track, but you got confused by the business wording, it happens. When you're solving these try and stay organized and write down every equation because things will get more complicated later in your math career.

profit = selling price - cost
p = r - c
given
p = 3
r = 12.5
plug back in and solve for cost
3 = 12.5 - c
c = $9.50

a = # of caramels
b = # of cremes

each box holds 30 pieces of candy
30 = a + b
a = 30 - b

cost = .25a + .45b
we're looking for a cost of $9.50 from earlier
9.5 = .25a + .45b

we have 2 equations and 2 variables we can use elimination now.
9.5 = .25(30 - b) + .45b
9.5 = 7.5 - .25b + .45b
2 = .2b
b = 10

plug b back into the other equation to solve for a
a = 30 - 10
a = 20
The box of candy should have 20 caramels and 10 cremes

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