algebra bean equation

[cula]

i have two types of bean, one cost $1/lb and the other cost $5/lb; I want to mix the two to get 50 lbs that cost $3/lb, how do you write the equation?

 

[masters]

i have two types of bean, one cost $1/lb and the other cost $5/lb; I want to mix the two to get 50 lbs that cost $3/lb, how do you write the equation?

Hi cula,

Make a table:

            Bean 1         Bean 2          Result
Cost        $1              $5                $3
Lbs          x              50 - x            50
------------------------------------------------------
Eq.          1x       +     5(50 - x)   =   3(50)

Edit: Thanks, lookagain.

 

[lookagain]

i have two types of bean, one cost $1/lb and the other cost $5/lb; I want to mix the two to get 50 lbs that cost $3/lb, how do you write the equation?

Hi cula,

Make a table:

            Bean 1         Bean 2          Result
Cost        $1              $5                $3
Lbs          x              50 - x            50
------------------------------------------------------
Eq.          1x       +     5(50 - x)   =   3(50)

masters,

I made a correction in your equation in the quote box above. It looked as if it were an accident (typo).

All, something to note is that $3/lb is the average of $1/lb and $5/lb. So there should
be equal numbers of pounds for the quantities being mixed to arrive at the 50 pounds
of mixture.

** However, do write out the proper algebraic equation(s) and solve it/them.

 

[masters]

Thanks, lookagain. I was more intent on lining everything up and typed the wrong number in the equation.

 

[mmm4444bot]

I realize that the table implicitly defines symbol x, but I like to see explicit definitions for all symbols in any word problem.

(I contributed to this thread yesterday, but my post is gone.)

 

[masters]

Re:

I realize that the table implicitly defines symbol x, but I like to see explicit definitions for all symbols in any word problem.

(I contributed to this thread yesterday, but my post is gone.)

The table explicitly defines x as the number of pounds of bean 1.

 

[mmm4444bot]

I printed the original post. I printed the table. I printed an explicit definition for the symbol x, in sentence form.

I took these three sheets of paper to the college, and I pestered about three dozen people in and about the Math Building's lounge and in the math lab, itself.

Not very scientific, yet after confirming that the respondent had intermediate-algebra experience I asked, "What do you think the symbol x represents, in this chart?" and recorded their response as either "correct or close enough" or "they haven't got a clue".

Subjects privvy to the printed definition answered correctly (or close enough) 94% of the time (16 out of 17).

Subjects shown only the exercise and chart answered correctly (or close enough) 69% of the time (11 out of 16).

 

[lookagain]

After I looked at it (not with its intent, but with the display), I see that the chart
is inconsistent with its constants and variables. In the first column under "Bean 1," it lists "$1x" for "Cost."
Under that it lists "x" for "Lbs." And under that it lists "1x" for the first term of the row indicated by "Eq."

Where the "1x" is has to be "$1x" instead. But as for usual streamlining in making a chart, a solver
would not write "$1" in the chart for the first place. There would be "1" written there.
This is shown in the amended chart below:

Hi cula,

Make a table:

            Bean 1         Bean 2          Result
Cost(in $)   1               5                 3
Lbs          x              50 - x            50
------------------------------------------------------
Eq.          1x       +     5(50 - x)   =   3(50)

\(\displaystyle Note: \ \ This \ \ still \ \ does \ \ not \ \ address \ \ that \ \ there \ \ are \ \ no \ \ let-statements \ \ about \ \ what \ \ "x" \ \\)

\(\displaystyle represents \ \ nor \ for \ \ what \ \ "50 - x" \ \ represents.\)