Functions: 342 items sold at $1.75/hotdog, $0.75/soda

dtmilo

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Jan 15, 2008
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write and solve the following functional equation:

Class sold hotdogs at $1.75 each and sodas for $.75 each. A total of 342 items were sold. A total of $293.00 was earned. Hotdogs are X and sodas are Y.....am I on the right path here???

x+y=342

f(x)=1.75x + .75y
f(x)= .25(7x+3y)
...now I'm lost.....Do I solve for y, where y=342-x
then put 1.75x + .75(342-x) = 293
1.75x + 256 - .75x = 293
x= 293 - 256.50
x=36.5

How many of each did they sell to have sold 342 and earn $293?
 
Re: FUNCTIONS

I don't think that one can sell a half of a hotdog.
Try this for your second equation: \(\displaystyle {175}x + {75}y = 29300\).
 
dtmilo said:
write and solve the following functional equation: Class sold hotdogs at $1.75 each and sodas for $.75 each. A total of 342 items were sold. A total of $293.00 was earned. Hotdogs are X and sodas are Y.
I will guess that you are supposed to find the number of hotdogs and sodas sold, as a function of one variable. (The problem statement is rather confusing. If the rest of your book is this badly written, your befuddlement is only natural.)

Use the given variable assignments:

. . . . .hotdogs sold: x

. . . . .sodas sold: y

. . . . .total number of items sold: x + y = 342

Then:

. . . . .y = 342 - x

Turning to the income:

. . . . .hotdog income: 1.75x

. . . . .soda income: 0.75y

. . . . .total income: 1.75x + 0.75y = 293

Now subsitute:

. . . . .1.75x + 0.75(342 - x) = 293

. . . . .1.75x + 256.5 - 0.75x = 293

. . . . .x + 256.5 = 293

....and so forth. I don't see how you're supposed to come up with a "function" for any of this...? And since you're going to end up with a fractional number of items, which of course makes no sense, I have a feeling this exercise contains typoes, too. :shock:

Eliz.
 
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