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Question 1093470: Hi appreciated tutors,
I cannot figure out this simple problem...
Tasha bought salads at $2.75 each and cartons of milk at $.80 each. The total cost was $16.15. How many of each did Tasha buy?
I tried to set the problem up like this:
X=number of salads, Y=number of milks
2.75X + .8Y = 16.15
X + Y = 3.55
I then tried to solve as a linear system problem but I just cannot get the correct values. The answers are X=5 and Y=3
Please help!! Thank you!!
Found 3 solutions by ankor@dixie-net.com, ikleyn, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Tasha bought salads at $2.75 each and cartons of milk at $.80 each.
The total cost was $16.15. How many of each did Tasha buy?
:
I tried to set the problem up like this:
X=number of salads, Y=number of milks
2.75X + .8Y = 16.15; this is right
But this one isn't
X + Y = 3.55
:
The problem here is the information gives us only 1 equation and two unknowns.
We can approach this using the fact that the solutions have to be integers
2.75x + .8y = 16.15
.8y = -2.75x + 16.15
divide both sides by .8
y = 
If you put this equation y= into your Ti83 or similar, then look at the table of values for x and y, you will see only one set of solutions are positive integers; x=5 and y=3
:
They should have given you more information there
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Answer. 5 salads and 3 cartons of milk.
Check. 5*275 + 3*80 = 1615.
Solution
You have ONE and ONLY ONE governing equation
2.75*X + 0.8*Y = 16.75.
And NO OTHER.
But since you are looking for INTEGER solutions X and Y only, it is ENOUGH to find them.
To solve it, multiply (for the sake of convenience) both sides by 20, to get all coefficients integer (including right side).
You will get
55X + 16Y = 323.
It is so called Diophantine equation, which means that the coefficients are integer number, and the solution,
which you are seeking for, is integer too.
It is solved, in this case, by the trial and error method.
I do it, using Excel in my computer.
I make one column of integer numbers x = 1, 2, 3, . . .
They are my "trials".
Then I make the second column of integers 323-55*x.
Finally, I make the third column of numbers Y =  .
And I make my table long enough.
Then I see where I get integer solution for Y = .
In this way I obtain the solution in 10 - 20 seconds.
*** Solved and explained ***
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Hi appreciated tutors,
I cannot figure out this simple problem...
Tasha bought salads at $2.75 each and cartons of milk at $.80 each. The total cost was $16.15. How many of each did Tasha buy?
I tried to set the problem up like this:
X=number of salads, Y=number of milks
2.75X + .8Y = 16.15
X + Y = 3.55
I then tried to solve as a linear system problem but I just cannot get the correct values. The answers are X=5 and Y=3
Please help!! Thank you!!
The way I do these types of problems where 2 variables are given but just 1 equation, is this:
I divide 16.15 by 2.75 to see the MAXIMUM number of salads that can be purchased since salads, at $2.75 is limited to a SMALLER range of integers.
When I do this, I get: 5.872727273, which means that the number of salads I can buy is between 1 and 5, inclusive.
When I multiply 2.75 by 5, I get $13.75. When I subtract $13.75 from $16.15, I get $2.40, and when I divide $2.40 by $0.80, I get 3.
If after subtracting $13.75 from $16.15, and dividing the result by $0.80, I DID NOT get INTEGERS, then I would've continued by multiplying 2.75 by 4, subtract that from $16.15,
and try to see if I'd get an integer value for the number of cartons of milk. I would've done this until I get to 1 salad, if itw's necessary.
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