Employees of an office ordered lunch from a local store, One day the order was for 4 hamburgers and 3 orders of fries, a total cost of $24. Another day, the order was for 6 hamburgers and l order of fries, for a total cost of $29. Set up equation and solve by elimination or substitution.

My equations are : 4h +3f=24 and 6h+1f+29 is this correct?

Quote:

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Originally Posted by floree

Employees of an office ordered lunch from a local store, One day the order was for 4 hamburgers and 3 orders of fries, a total cost of $24. Another day, the order was for 6 hamburgers and l order of fries, for a total cost of $29. Set up equation and solve by elimination or substitution.

My equations are : 4h +3f=24 and 6h+1f+29 is this correct?

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No. Almost correct. It is : 4h +3f=24 (1) and 6h+1f = 29 (2)

Additional
Solution for f :
(1) all parts times 3 :
(2) all parts times 2 :
(1) 12h + 9f = 72
(2) 12h + 2f = 58
-------------------- -
--- 00h + 7f = 14
7f = 14 --> 1f = 14/7 --> 1f = 2

And solution for h :
4h + 3f = 24
4h + 6 = 24
4h = 24 - 6 = 18
1h = 18/4 = 4,50 --> 1h = 4,50

Quote:

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Originally Posted by floree

My equations are : 4h +3f=24 and 6h+1f+29 is this correct?

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The first equation is right but the second one should be : 6h+1f=29 because 29 is the total cost. Solving them simultaneously through elimination can be done like this:

4h + 3f = 24
6h + 1f = 29

-4h - 3f = -24
18h + 3f = 87

- 4h + 18h = -24 + 87

14h = 63
h = 63/14 = 4.5

4(4.5) +3f = 24
f = (24-18)/3 = 6/3 = 2

h = 4.5, f = 2

You'll see that using substitution will give you the same answer. If you want to do it through substitution, this is how to do it:

4h + 3f = 24
6h + f = 29

f = 29 - 6h

4h + 3(29-6h) = 24
4h + 87 - 18h = 24

And we are left with the same single equation we saw before in the elimination method. Solving completely will get you the same answer.

Quote:

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Originally Posted by floree

Employees of an office ordered lunch from a local store, One day the order was for 4 hamburgers and 3 orders of fries, a total cost of $24. Another day, the order was for 6 hamburgers and l order of fries, for a total cost of $29. Set up equation and solve by elimination or substitution.

My equations are : 4h +3f=24 and 6h+1f+29 is this correct?

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A reaction to an answer is always much appreciated, even if it does not solve your specific problem...
:)