A farmer grows two types of grain in his fields. He has a seed budget of $17,000.00 and has spent $9,200.00 to plant wheat seed so far. If barley seed costs $41.00 per acre to plant, what is the maximum number of acres of barley the farmer can plant and still be under budget?

190 acres
414 acres
191 acres
224 acres

Question

A farmer grows two types of grain in his fields. He has a seed budget of $17,000.00 and has spent $9,200.00 to plant wheat seed so far. If barley seed costs $41.00 per acre to plant, what is the maximum number of acres of barley the farmer can plant and still be under budget?

 190 acres
 414 acres
 191 acres
 224 acres

zepdrix · Answer

Let the number of unknown acres be x.

Then if each acre costs 41 to seed,
then x acres will cost 41x.

This is the cost to seed x acres of farm: 41x.

Let's add to this, the amount he's already spent: 9200.

41x+9200

This amount must not exceed farmer Billy's budget: 17000.
So we're saying this amount must be `equal or less than` the budget amount.

$\large\rm 41x+9200\le17000$

zepdrix · Answer

Solve for x.
It has 9200 being added, so we'll undo that by subtracting 9200 from each side,$$\large\rm 41x+9200-9200\le17000-9200$$$$\large\rm 41x\le7800$$

zepdrix · Answer

What next?
41 is `multiplying` the x. How do we undo multiplication?

Hmm any ideas?

bayleejadee · Answer

@zepdrix with division?

zepdrix · Answer

Yes, division is the opposite of multiplication.
That seems like a good idea.
So we divide by 41,$$\large\rm \frac{\cancel{41}x}{\cancel{41}}\le\frac{7800}{41}$$

zepdrix · Answer

$$\large\rm x\le 190.244$$

zepdrix · Answer

So farmer Billy Bob can afford to seed 190.244 acres, but no more than that.
So which option should he choose?

bayleejadee · Answer

190 acres (:

zepdrix · Answer

because 191 would be too much?

Yayy good job \c:/