Need help to figure out this Inequality question

Question

A candy store sells boxes of candy containing caramels and cremes. each box sells for $12.50 and holds 30 pieces of candy(all pieces are the same size). if the caramels cost $0.25 to produce and the cremes cost $.045 to produce, how many should be in a box to make a profit of $3?

Answer 1

Problem should be corrected to read each caramel costs $0.25 and each creme costs $0.045 to produce.

and we want to make the profit at least $3 per box. More than likely, it shouldn't cost so much more to make a caramel and the price of one caramel's production was probably mistyped and should be $0.025.

let a = number of caramels

let b = number of cremes

Both together a + b must total 30........................ a + b= 30

Production costs are 0.25a+ 0.045b

Selling price is $12.50

Selling price - profit = production costs.............. 12.50 - 3 = 0.25a + 0.045b

Subtract on left side 9.50 = 0.25a + 0.045b

Use 1st equation to solve for a

a + b = 30 a = 30 - b which you can put into 2nd equation, leaving

9.50 = 0.25(30 -b) + 0.045b

9.50 = 7.5 - 0.25b + 0.045b

9.50 = 7.5 - 0.205b Subtract 7.5 on each side (treat left and right EQUALLY)

2 = - 0.205 b

-9.75 = b and a = 30 - b = 30 + 9.75 = 39.75

although -9.75 cremes and 39.75 caramels do add up to 30 candies, you'd have to slice some and vaporize others to make it work. Therefore, the problem was mistyped. Repeat replacing the 0.045 with 0.45, more in line with the cost of the caramels at 0.25. Anyway, cremes are more complicated than caramels, so there.

Check 10 cremes @ 0.45 = 4.50 production costs

20 caramels @ 0.25 = 5.00 production costs

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9.50 total production costs with $3 profit = 12.50 selling price

How many should you put in a box? Simple answer to a simple question is 30.

If it would ask how many of each kind should be put in the box, we can definitively say 10 cremes and 20 caramels.