SOLUTION: Three bags of potatoes and four cases of corn cost $40. Five bags of potatoes and two cases of corn cost $34. Find the cost of one bag of potatoes and the cost of one case of corn.

Question 966770: Three bags of potatoes and four cases of corn cost $40. Five bags of potatoes and two cases of corn cost $34. Find the cost of one bag of potatoes and the cost of one case of corn. [Show or explain the procedure used to obtain your answer.]
Found 3 solutions by josgarithmetic, checkley77, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Variable quantities are the prices for the corn and potatos.
p, dollars per bag for potatos;
c, dollars per case for corn;

Solve the system in any way you know. Elimination method may be good for a start if you take the second equation and use as .
Answer by checkley77(12844)   (Show Source): You can put this solution on YOUR website!
3P+4C=40
5P+2C=34 MULTIPLY BY -2 & ADD.
3P-4C=40
-10P-4C=-68
------------
-7P=-28
P=-28/-7
P=$4.00 COST PER BAG OF POTATOES.
3*4+4C=40
12+4C=40
4C=40-12
4C=28
C=28/4
C=$7.00 PER CASE OF CORN
PROOF:
5*4+2*7=34
20+14=34
34=34
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!

Let x be the price of one bag of potatoes and y be the price of one case of corn.

Then you have the system of two linear equations

.

Use the elimination method to solve this system. For it, multiply the second equation by 2 and subtract the first equation. You will get

  10x + 4y = 68
-
   3x + 4y = 40
-------------------------
   7x        = 68-40 = 28.

So, x = = 4.

Now, substitute the found value of x into the first equation of your system. You will get

3*4 + 4y = 40,

or

4y = 40 - 12 = 28.

Hence, y = = 7.

Answer. The cost of one bag of potatoes is $4 and the cost of one case of corn is $7.

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