SOLUTION: A vendor at the county fair wishes to spend $312 on his milkshake booth and has a goal of earning $1410. He figures he can make a small shake for $0.45 and a large shake for $0.75.

Question 166079: A vendor at the county fair wishes to spend $312 on his milkshake booth and has a goal of earning $1410. He figures he can make a small shake for $0.45 and a large shake for $0.75. He plans to sell a small shake for $2.25 and a large shake for $3.00. Write and solve a system of equations to determine how many of each size shake he will need to make and sell in order to reach his goal.
Okay my teacher is a crazy lunatic and thinks i am super smart by giving me a super hard question, and i struggle with math in the first place. I understand that i need to find the x and y varibles but im not sure where to begin. theres the amount of money he needs to make a shake and then the amount that hes going to sell them for. am i correct?.... oh and this isnt in my book. he just makes them up randomly.

Found 2 solutions by elima4, Mathtut:
Answer by elima4(15) (Show Source): You can put this solution on YOUR website!
I'm sure your teacher is not crazy.:)
Anyway, I'll try and help;
First of all we know he spends $312 all together. Now lets break that down. To make small milkshakes it cost .45 for each, and for large it cost .75 for each.
So the equation would be;
x = small milkshakes
y = large milkshakes
.45x + .75y = 312
Now the lther equation;
We know he wants to make $1410 altogether, he charges 2.25 for small and 3.00 for large.
So the equation;
2.25x + 3y = 1410
Now we have our two equations, lets solve them.
.45x+.75y = 312
2.25x+3y = 1410
========================
let solve the first for y;
.75y = 1410-.45x

y= 416-.6x
Now plug this into either equation for y to find x;
2.25x +3(416-.6x)=1410
2.25x + 1248 - 1.8x=1410
.45x+1248=1410
.45x=162
x=360
Now we have our x, lets find out y;
.45(360)+.75y=312
162 + .75y = 312
.75y = 150

y=200
Check
.45(360) + .75(200)=312
Hope you understand
:)
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
I am sorry, but I think something is missing in this problem ...at least the way it is written. The cost of the booth is a fixed cost of $312 dollars that vendors must spend in order to operate at a fair and $1410 is a fixed amount that the vendor would like to earn. We can only really generate one equation here with 2 variables as far as I can see
and that would be if A were the number of small milkshakes
............ and B were the number of large milkshakes
then (2.25-.45)A + (3.00-.75)B = $1410+312 (amount you want to make plus fixed costs) so 1.80A+2.25B=1522.
we need more information to solve this in my opinion.
SO MAYBE YOUR TEACHER IS CRAZY EITHER THAT OR I AM....LOL
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