Question 950665: I am not very good with word problems, and my parents can't help me right now because they are busy, but i think i have a start and i was hoping to confirm my structure of solving this question.
At Happy Burger you can get one order of fries and one burger for $7.20. You can also get three orders of fries and seven burgers for $38.60. What is the cost of each item?
1x + 1y = 7.20
[-1x -1x]
y = -1x + 7.20
3x + 7y = 38.60
[-3x -3x]
7y = -3x + 38.60
[/7 /7 /7]
y = -3/7x + 5.51
Found 3 solutions by Theo, ankor@dixie-net.com, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you're on the right track.
it's one way to solve the problem.
there are others.
i'll follow your logic and finish it for you.
x = cost of fries.
y = cost of burger.
1x + 1y = 7.20
subtract 1x from both sides of the equation to get:
y = 7.20 - x
3x + 7y = 38.60
subtract 3x from both sides of the equation to get:
7y = 38.60 - 3x
divide both sides of the equation by 7 to get:
y = 38.60/7 - 3x/7
simplify to get:
y = 5.51 - 3x/7 *****
***** note that you rounded the intermediate results. this will cause a rounding error in the final result.
you have two equations that need to be solved simultaneously.
they are:
y = 7.20 - x
y = 5.51 - 3x/7
replace y in the second equation with 7.20 - x in the first equation to get:
7.20 - x = 5.51 - 3x/7
subtract 5.51 from both sides of the equation and add x to both sides of the equation to get:
7.20 - 5.51 = x - 3x/7
simplify to get:
1.69 = 4x/7
multiply both sides of the equation by (7/4) to get:
7/4 * 1.69 = 4/7 * x * 7/4 which becomes:
2.96 = x *****
***** it's actually equal to 2.9575 which was rounded to 2.96. once again, rounding the intermediate results can result in a rounding error when you get to the final result.
that's the cost of the fries.
since x + 7 = 7.20, the cost of the burger must be 7.20 - 2.96 = 4.24
that satisfies your first equation.
your second equation is 3x + 7y = 38.60
replace x with 2.96 and y with 4.24 to get:
3 * 2.96 + 7 * 4.24 = 38.60
solve the equation to get:
38.56 = 38.60
since you rounded your intermediate results to 2 decimal places, the answer won't necessarily be right on, but it's close enough to indicate that you did it right.
another way to solve the equation would have been:
x + y = 7.20 (first equation)
3x + 7y = 38.60 (second equation)
multiply the first equation by -3 to get:
-3x - 3y = -21.60 (first equation multiplied by -3)
3x + 7y = 38.60 (second equation)
add the equations together to get:
4y = 17
solve for y to get y = 4.25
since x + y = 7.20, then x must be equal to 7.20 - 4.25 = 2.95
x + y is equal to 720.
3x + 4y is equal to 3*2.95 + 7*4.25 = 38.60
this method got you the the exact answer because none of the intermediate results were rounded.
that won't always happen, but it did in this case.
with the first method, if you didn't round the intermediate results, you would have gotten the same answer as well.
rounding the intermediate results leads to possible errors in the final result.
rounding is only recommended when you get to the final results.
try not to round the intermediate results.
if you have to, then round to more decimal places than the final result will be rounded to.
in this case, if you had rounded to 5 decimal places, you would probably have been right on in the final result using either method.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! At Happy Burger you can get one order of fries and one burger for $7.20. You can also get three orders of fries and seven burgers for $38.60. What is the cost of each item?
1x + 1y = 7.20
[-1x -1x]
y = -1x + 7.20
:
3x + 7y = 38.60
Replace y with (-x+7.20)
3x + 7(-x+7.20) = 38.60
distribute
3x - 7x + 50.4 = 38.60
3x - 7x = 38.60 - 50.40
-4x = -11.80
x = -11.80/-4
x = $2.95 is the price of the fries
Find the price of the burger
7.20 - 2.95 = $4.25 for the burger
:
:
Check this out using your 2nd equation
3(2.95) + 7(4.25) =
8.85 + 29.75 = 38.60
Answer by MathTherapy(10552)  (Show Source):
|
|
|
