Word problem on math

Question

sarah owns a speciality cand store selling two types of boxes imported chocolate the 4you box is $75 each box and he makes a profit of $30 on each box. the crave4 is 100 per box, and he makes profit of $40 each box . expects to sell at least 80 boxes total this month. but she needs to make at least 2,950 profit on them

Answer 1

I tend to start this type of question by defining some variables.

So, let's say y is the number of 4you boxes sold.

And c can be the number of crave boxes sold.

If Sarah sells just the 4you boxes, she'll make (30)(80) dollars in profit. $2400

If Sarah sells just the crave boxes, she'll make (40)(80) dollars in profit. 3200

Obviously, she'll want to sell more crave boxes, but that's not the point.

If she sells some mixture, then she'll earn 30y+40c dollars, which we want to be at least 2950.

The trick to this type of problem is defining one variable in terms of the other. To do that, we'll say that

c+y = 80. (Technically, it's c + y is greater than or equal to 80, by your question, but we're finding a minimum, so it's fine to look at the equals case.)

From c+y = 80, we'll solve for a variable. I like solving for y here, but you can solve for c if you want.

y = 80 - c.

Substitute that into the profit equation/inequality and we get

30(80 - c) + 40c > 2950

Distribute

2400 - 30c + 40c > 2950.

Combine like terms

2400 + 10c > 2950

Get the variable by itself

10c > 550

So, c > 55 (with y being 25 at that point).

Message me if your teacher wants a graph with this.