SOLUTION: The word problem in question is..... Phil is making a starbucks run or his exhausted Math 105 classes. He is going to buy a combination of lattes and cappuccinos. The lattes cost

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Question 117592: The word problem in question is.....
Phil is making a starbucks run or his exhausted Math 105 classes. He is going to buy a combination of lattes and cappuccinos. The lattes cost $4 each and the Cappucinos cost $3 each. If he needs 30 drinks total and has $100 to spend how many of each should he buy.
I have figured out that he should buy 20 cappuccinos at $3 each and 10 lattes at $4 each which totals $100.00
The trouble that I have run into is I cant figure out how I got that and what formula to set up for this probelm.
Can you please help? Thank you so much!!!!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Phil is making a starbucks run or his exhausted Math 105 classes. He is going to buy a combination of lattes and cappuccinos. The lattes cost $4 each and the Cappucinos cost $3 each. If he needs 30 drinks total and has $100 to spend how many of each should he buy.
I have figured out that he should buy 20 cappuccinos at $3 each and 10 lattes at $4 each which totals $100.00
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Let # of lattes be "t"; Let # of Cappus be "c"
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EQUATIONS:
4t+3c= 100
t+c = 30
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Multiply thru the 2nd equation by 3 to get:
3t+3c=90
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Subtract from the 1st equation to solve for "t":
T = 10 (# of lattes)
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Substitute into t+c=30 to solve for "c"
10 + c = 30
c = 20 (# of cappus )
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Cheers,
Stan H.