I need help with the word problem in the description

Question

At a vegetable stand, you bought 3 pounds of peppers for $4.50. Green peppers cost 1$ per pound and orange peppers cost 4$ per pound. Find how many pounds of each pepper you bought.

Answer 1

If possible, assign variables to the values the problem asks you to find:

  x = pounds of green peppers

  y = pounds of orange peppers

 

Translate:

  "you bought 3 pounds of peppers"   means x + y = 3

  "Green peppers cost 1$ per pound and orange peppers cost 4$ per pound ... for $4.59"       means

      ($1)x + ($4)y = $4.50

  "Find how many pounds of each pepper you bought."     means   report x,y

 

Now, the easy mathL

      x + 4y = 4.5

      x +  y  = 3

    ----------------     (use elimination method;  subtract equations)

            3y = 1.5

              y = 0.5

 

     x + y = 3

           y = 0.5

   ----------------       (elimination method again; subtract equations)

     x       = 2.5

 

Checking (very important):

  Is   2.5 + 0.5 = 3  ?    yes

 

  Is  (1)(2.5) + (4)(0,5) = 4.50     ?

         2.5 + 2 = 4.50    ?

            4.5  =  4.5     ?  yes

Answer 2

Hi Peggy

 

This is one of those problems that requires you to set up 2 equations

 

Let's say X is the number of pounds of green peppers and Y is the number of pounds of orange.  You know right away that X + Y = 3 because that is the total pounds of peppers you bought.  You also know that 1X + 4Y = 4.50 is what you spent.

 

The trick is to take your equation of X + Y = 3 and solve for X making it X = 3 - Y.  Now that you have that you can insert that into the other equation for X

 

So 1X + 4Y = 4.50 becomes 3-Y + 4Y = 4.50

 

Now solve for Y

 

3 + 3Y = 4.5

3Y = 1.5

Y = 0.5 - so you bought 1/2 a pound of orange peppers which means you bought 3 - 0.5 = 2.5 pounds of green peppers

 

go back and check that it makes sense dollar-wise

 

1(2.5) + 4(.5) = 4.5

2.5 + 2 = 4.5

4.5 = 4.5

 

good to go!

 

All the best

 

Lori