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.
i need an inequality and how many more boxes of oranges he will need to make up the difference.
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
To determine if the farm will earn at least $4,000, we need to calculate the total revenue from selling boxes of oranges and grapefruits.
The revenue from selling 210 boxes of oranges is 210 * $8 = $1680.
The revenue from selling 150 boxes of grapefruits is 150 * $12 = $1800.
To find out if the total revenue is at least $4,000, we need to add these two amounts:
Total revenue = Revenue from oranges + Revenue from grapefruits
Total revenue = $1680 + $1800
Total revenue = $3480
Since the total revenue is less than $4,000, we need to calculate how much more revenue is needed. Let's represent the number of additional boxes of oranges the farm needs to sell as 'x'. Each additional box of oranges sold will add $8 to the revenue. Therefore, the additional revenue from selling 'x' boxes of oranges can be represented as 8x.
The inequality to represent the situation is:
Total revenue + Additional revenue ≥ $4,000
$3480 + 8x ≥ $4,000
To solve the inequality, subtract $3480 from both sides:
8x ≥ $4,000 - $3480
8x ≥ $520
Now, divide both sides of the inequality by 8:
x ≥ $520 / 8
x ≥ 65
Therefore, the farm must sell at least 65 more boxes of oranges to make up the difference and earn at least $4,000.