SOLUTION: Three burritos and two tacos cost $11.50, and two burritos and three tacos cost $11. How much does one taco cost?

Question 430705: Three burritos and two tacos cost $11.50, and two burritos and three tacos cost $11. How much does one taco cost?
Found 3 solutions by jorel1380, stanbon, oberobic:
Answer by jorel1380(3719)   (Show Source): You can put this solution on YOUR website!
Let's call burritos X, and tacos Y. Then
3X+2Y=11.50
2X+3Y=11.00
Let's multiply the first equation by 3, and the second by 2:
9X+6Y=34.50
4X+6Y=22.00
Subtract the 2nd equation from the 1st:
5X=12.50
X=2.50
Y=2.00
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Three burritos and two tacos cost $11.50, and two burritos and three tacos cost $11. How much does one taco cost?
--------------
Equations:
3b+2t = 1150 cents
2b+3t = 1100 cents
------
Multiply top eq by 2
Multiply bottom eq by 3
----
6b + 4t = 2300
6b + 9t = 3300
-----------------
Subtract and solve for "t":
5t = 1000
t = 200 cents or $2.00 (price of one taco)
================
Cheers,
Stan H.
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!
B = price of a burrito
T = price of a taco
.
3B + 2T = 11.5
2B + 3T = 11
.
Now we have simultaneous equations that have to be solved, which is a bit tedious, but cannot be avoided.
.
Multiply the first equation by 2 across both sides:
6B + 4T = 23
.
Multiply the second equation by 3 across both sides
6B + 9T = 33
.
Now we can do the arithmetic...
6B + 4T = 23
6B + 9T = 33
.
Subtract the 2nd equation from the 1st.
.
-5T = -10
Divide both sides by -5
T = 2, which means each taco cost $2.
.
Substitute T=2 into one of the prior equations:
3B + 2T = 11.5
3B + 2(2) = 11.5
3B + 4 = 11.5
Subtract 4 from both sides.
3B = 7.5
Divide both sides by 3
B = 2.5, which means each burrito cost $2.50
.
To check your work, substitute these values into the other equation:
2B + 3T = 11
2(2.5) + 3(2) = 5 + 6
5+6 = 11
That checks.
.
Now refer to the question to be sure to state your answer clearly.
Answer: One taco costs $2.00.
.
Done.
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