Question 640035: Suppose you have a budget of 400 dollars for one month. You would like to buy some textbooks and CDs.
The average cost of a book is 55 dollars each and that of a CD is
13 dollars each. Let x denote the number of books you buy and y denote the
number of CDs that you buy. Write the equation of your budget constraint in the form y=mx+b, where m and b are some numbers.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Constraints are inequalities, not equations. Furthermore, given the cost data provided and the fact that you can't buy fractional parts of either CDs or books, there is no combination of $13 items and $55 items that total $400 -- which is simply more evidence that this should be an inequality rather than an equation.
What would have been appropriate is to ask you to write the equation, in slope-intercept form, that represents the boundary line of the budget constraint inequality solution set half-plane. Such an equation would have the form 
If  represents the number of books purchased, then the total cost of those $55 books is  . Likewise the total cost of the CDs purchased is  .
Then, since the budget is $400, meaning that you cannot spend MORE than $400, but you can always spend LESS, the constraint inequality is:
An equation of the boundary line of the constraint inequality is found by replacing the inequality sign with an equals sign.
Then add  to both sides and multiply both sides by  to put the equation into slope-intercept form.
John
My calculator said it, I believe it, that settles it
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