SOLUTION: A candy company sells premium chocolate at $5 per pound and regular chocolates at $4 per pound. If Barrett buys a 7-pound box of chocolates that costs him $31, how many pounds of p

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Question 1208492: A candy company sells premium chocolate at $5 per pound and regular chocolates at $4 per pound. If Barrett buys a 7-pound box of chocolates that costs him $31, how many pounds of premium chocolates are in the box?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
A candy company sells premium chocolate at $5 per pound and regular chocolates at $4 per pound.
If Barrett buys a 7-pound box of chocolates that costs him $31, how many pounds of premium chocolates are in the box?
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Let x be the number of pounds of premium chocolates in the box.

Then the number of pounds of regular chocolates in the box is (7-x).


Write the cost equation for the box of chocolates

    5x + 4*(7-x) = 31  dollars.


Simplify and find x

    5x + 28 - 4x = 31

    5x - 4x = 31 - 28

        x   =    3.


ANSWER.  There are 3 pounds of the premium chocolate in the box.


CHECK.   The total cost of the box is then  5*3 + 4*(7-3) = 15 + 4*4 = 15 + 16 = 31 dollars.   ! correct !

Solved.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor supplied a response showing a typical formal algebraic solution -- which is probably what you were looking for.

But solving problems like this informally (and mentally), using logical reasoning and simple arithmetic, is good brain exercise.

For this particular kind of problem, the method shown below is useful.

If all 7 pounds were regular chocolates, the total cost would be 7($4) = $28.
But the actual cost is $31, which is $3 more.
Each pound of premium chocolates costs $1 more than each pound of regular chocolates, so the number of pounds of premium chocolates is $3/$1 = 3.

ANSWER: 3