Another word problem: how many of each coffee should he buy?

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This is what I have but when I worked it out it was inconceivable so I know I did something wrong. Please help. Andrea

Phil is making a Starbuck’s ® run for his exhausted Math 105 classes. He is going to buy a combination of Lattes and Cappuccinos. The Lattes cost $4 each and the Cappuccinos cost $3 each. If he needs 30 drinks total and has $100 to spend, how many of each should he buy?

Lattes - $4 each - Quantity is x - Total is 4x
Cappuccinos - $3 each - Quantity is 30-x - Total is 3(30-x) or 90-3x
Mixture - $100 to spend - Quantity is 30 - Total is 3000

So then I said 4x+90-3x=3000
x=2910

I think I have the right idea but obviously it doesn't work.
 
x = number of Latte's

money spent on Latte's = 4x

30-x = number of Cappuccino's

money spent of Cappuccino's = 3(30-x)

total money spent = 100

4x + 3(30-x) = 100

solve for x, then determine the value of 30-x.
 
Wow, I was making it so much harder than it should have been. Can please tell me if this is the correct way to do the problem? Thanks!! Andrea

Lattes - $4 / x / 4x
Cappuccinos / $3 / 30 - x / 3(30 - x)

4x + 90 – 3x = 100
x = 10 = Lattes to buy
30 – x = 20 = Cappuccinos to buy
 
come on, check the solution yourself ... how much will it cost to purchase all 10 + 20 = 30 drinks that you calculated?
 
I figured it after I posted it...sorry. It comes to exactly $100. :D

Andrea
 
In the future, please post follow-ups to old posts to the originating threads, rather than posting the same question twice.

Thank you.

Eliz.
 
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