Word Problem

Question

Mrs. Lewis needs to buy two types of grain, oats, and barley to mix as a feed supplement for her cattle. She has $4275 to spend on grain and wants the mixture to be 3 parts oats and 2 parts barley. She can buy oats for $1.10 per bushel and barley for $2.10 per bushel. Mrs. Lewis needs 7,000 bushels of grain. How many bushels of barley should she buy?

Answer 1

This is an old question, but worth some explanation. I had fun reading some of the answers here; the problem statement is obviously a prank!

 

These types of problems are units of measurement problems and are solved as Daniel did.

 

 

The units need to be consistent. While Daniel attempted to keep the quantity and the $$ separate, and got the end result correct, the units got mixed up.

 

 

The problem should be written as:

one bushel of grain = 3 sacks of oats + 2 sacks of barley => 7,000 bushels = 3x + 2y (x,y expressed in sacks)

cost of oat = $1.10/sack ; cost of barley = $2.10/sack => $4,275 = 1.10x + 2.10y (x,y expressed in sacks)

 

The problem statement therefore is:

How many sacks of oat and barley does Mrs Lewis need to buy? (parts got everyone confused - haha)

 

 

The solution is solved in sacks, certainly not in bushels. Only in this way can it be solved as Daniel describes it.

 

 

If the unit of measurement for oat and barley is bushels, the problem is not solvable, as some had fun pointing out.

 

 

A 2 equation problem involves 3 units of measure. in this case:

equation 1 : bushel/sack

equation 2: $/sack

 

The three units being $, bushels and sacks (or parts)

 

 

I hope no student followed this thread - lol

 

 

Answer 2

Mrs. Lewis cannot buy 7,000 bushels of grain, for that would cost her at least 7,000*$1.10=$7,700, but she only has $4275.

Let X=bushels of oat and Y=bushels of barley. 3 parts oats and 2 parts barley means 2X=3Y, or X=1.5Y. Her cost is 4275=1.1X+2.1Y. Now substitute X=1.5Y and simplify: 4275=1.1(1.5Y)+2.1Y=3.75Y. Therefore, Y=4275/3.75=1140, so she should buy 1140 bushels of barley.

Answer 3

This problem is not a math problem, but an economic's problem. What do you do when you're over budget? There isn't a simple answer to that!

7000 bushels of grain, even if all the grain is the less expensive $1.10/bushel of oats will cost a lot more then $4275.00!

It's time to sell some livestock.

Answer 4

O = # of bushels of oats

B = # of bushels of barley

O+B = 7,000 ......(1)

O = (3/5)*7,000 = 4,200 bushels of oats

B = (2/5)*7,000 = 2,800 bushes of barley

But these cost 4,200*1.10 + 2,800*2.10 = $10,500. So, she needs to borrow 10,500-4,275 = $6,225 to buy 7,000 bushes of grain.

 

Answer 5

Let x be the oats and y be the barley. Keep the mix requirements with the grain and the $$$ with the $$$.

She needs a total of 7000 bushels of grain which is composed of 3 parts oats and 2 parts barley, thus:

3x + 2y = 7,000

In addition you are told that she has a finite dollar amount she can spend, $4275 where the oats are $1.10/bushel & $2.10/bushel, thus:

1.1x + 2.1y 

Now you have 2 unknown values and  equations:

3x+2y=7000 (Eq 1)
1.1x+2.1y=4275 (Eq2)

There are a couple of ways to go about this...find a common coefficient and subtract one equation or solve either equation for x or y and plug it into the other equation. Either way there will be fractions. I am going to solve for y in Eq 1 since it has whole numbers and plug that into Eq 2:

3x+2y=7000 -> 2y=7000-3x -> y= (7000-3x)2 -> y=3500-1.5x  (**)

Now plug y into Eq 2

1.1x+2.1y=4275 -> 1.1x + 2.1(3500-1.5x) -> 1.1x + 7350 - 3.15x = 4275 -> 7350 -2.05x = 4275
-> 2.05x = 3075 -> x = 3075/2.05 -> x=1500

Now that you have x=1500 plug that into Eq 1 or Eq 2 to find...you already solved Eq 1 for y earlier (**)  so that would be easiest to use:

(**) y = 3500 - 1.5x -> y = 3500 - 1.5(1500) -> y = 3500 - 2250 -> y = 1250

1500 bushels of oats and 1250 bushels of barley. Plug these numbers into either equation to verify. I don't have a calculator on me (hence my taking the whole number path!) so I will leave this to you.

Good luck and I hope it helped!

v/r

Daniel

Answer 6

Let's assume, that Mrs. Lewis will buy "x" bushels of oats, and "y" bushes of barley, then:
x + y = 7000 .......... (1)
1.1x + 2.1y = 4275 ....... (2)
xy < 0
(x, y) e Ø