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Question 148918: For Monday mornings staff meeting, Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $9.75 (excluding sales tax). For Fridays meeting, he bought 4 bags of bagels and 2 packages of cream cheese and paid $12.50 (again, excluding sales tax). How much do bags of bagels and packages of cream cheese cost?
Answer by mangopeeler07(462)   (Show Source):
You can put this solution on YOUR website! x=cost of bagels (in cents)
y=cost of cream cheese (in cents)
coefficient=quantity
Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $9.75:
2x+3y=975
He bought 4 bags of bagels and 2 packages of cream cheese and paid $12.50:
4x+2y=1250
So you have two equations:
2x+3y=975
4x+2y=1250
Multiply the first equation by negative two:
-4x-6y=-1950
4x+2y=1250
Add the equations
-4y=-700
You have successfully eliminated x from the equation (for now).
Divide by -4
y=175
That is the cost of the cream cheese in cents. Plug that back into either original equation, how about the first one:
2x+3(175)=975
Simplify
2x+525=975
Subtract 525 from both sides
2x=450
Divide by 2
x=225
That is the cost of the bagels in cents.
So,
1 Package of Cream cheese=$1.75
1 Bag of Bagels=$2.25
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