Question 1173443: Elizabeth wishes to purchase $3 boxes of cookies and $5 boxes of cookies. She decides to buy 4 fewer $5 boxes than $3 boxes. How many of each box can she buy for no more than $20?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number of 3 dollars boxes.
let y = the number of 5 dollar boxes.
your equation will be 3x + 5y <= 20
the number of 5 dollars boxes is 1 less than the number of 3 dollars boxes.
the equation for that is y = x - 4
in the equation of 3x - 5y <= 20, replace y with x - 4 to get 3x + 5(x-4) <= 20
simplify this equation to get 3x + 5x - 20 <= 20
add 20 to both sides of this inequality and combine like terms to get 8x <= 40
solve for x to get x <= 5
since y = x - 4, then y <= 1
when x = 5, y = 1
3x + 5y <= 20 becomes 3*5 + 5*1 <= 20 which becomes 20 <= 20 which is true.
any value of x < 5 will result in y being equal to 0.
if she wants at least one 5 dollar box, then x must be equal to 5.
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