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A farm sells boxes of oranges for $8 and boxes of grapefruits for $12. The farm wants to ear at least 4,000.

If he sells 210 boxes of oranges and 150 boxes of grapefruit will he earn at least $4,000? If not how many more boxes of oranges must he sell to make up the difference? Write an inequality to represent the situation.

  • math -

    so what is your question?

  • math -

    i need an inequality and how many more boxes of oranges he will need to make up the difference.

  • math -

    well, do it this way (it is called linear programming).

    Take a piece of paper, and make a large graph. On the horizontal axis, label that grapfruits. Scale starting at zero and ending at 400. On the vertical scale, label it oranges, acale from zero to 500.

    After you do that, then

    now, if the person sold only grapefruit, to get 4000 dollars, he would sell (4000/12 = 333 boxes. Label that point on the horizontal axis. On the vertical axis, label the max number of oranges (4000/8=500) Now connect those two points with a line. To sell 4000 dollars worth, he must be on the line, if to the right, he sells more, if to the left, he sells less.
    Now, to answer the question about how many more oranges. Go from the point 150,210 upward till you are at the line you drew. The distance upward is the number of additional oranges.
    Now for the inequality, look at the line you drew. oranges/500 + grapefruit/333 >= 1 check that

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