Question 1205478: The Harnapps and the Curies are going to the Pizza Palace for dinner. The Harnapps order 3 slices of pizza and 3 colas and have a bill that totals $15. The Curies order 4 slices of pizza and 3 colas and have a bill that totals $18. Determine the best method to solve the system of equations. Then
solve the system.
Found 3 solutions by Theo, math_tutor2020, josgarithmetic:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! harnapps ordered 3 pizza and 3 colas for 15 dollars.
curies ordered 4 pizza and 3 colas for 18 dollars.
since they both ordered 3 colas, then the only difference was curies ordered one extra pizza, so the cost of a pizza had to be 3 dollars because that was the difference in what they paid (18 dollars minus 15 dollars = 3 dollars).
if the pizza was 3 dollars, then harnapps total bill was 15 minus 9 dollars for pizza = 6 dollars for cola.
since they had 3 colas, then the cost of a cola had to be 2 dollars.
to solve this algebraically, you would do the following.
let x = cost of one pizza and y = cost of one cola.
your two equations are:
3x + 3y = 15
4x + 3y = 18
subtract the first equation from the second to get x = 3.
that means cost of a pizza was 3 dollars.
replace x with 3 in either equation and solve for y.
4x + 3y = 18 becomes 4*3 + 3y = 18 which becomes 12 + 3y = 18.
subtract 12 from both sides of the equation to get 3y = 6
solve for y to get y = 2.
solution is cost of a pizza is 3 and cost of a cola is 2.
3x + 3y = 15 becomes 3*3 + 3*2 = 15 which becomes 9 + 6 = 15 which becomes 15 = 15 which is true.
4x + 3y = 18 becomes 4*3 + 3*2 = 18 which becomes 12 + 6 = 18 which becomes 18 = 18 which is also true.
this confirms the solution is good.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
If you want to use elimination, then follow tutor Theo's approach when using algebra.
Substitution is another possibility.
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Here's a way to do it with mental math.
Both families ordered 3 colas. The only difference is that the Curies ordered 1 extra slice of pizza. So each slice of pizza must be 18-15 = 3 dollars, since we just look at the difference of their bills.
Harnapps:
3 slices = 3*3 = 9 dollars
15-9 = 6 dollars spent on colas, so each cola is 6/3 = 2 dollars
Curies:
4 slices = 4*3 = 12 dollars
18 - 12 = 6 dollars spent on colas, so each cola is 6/3 = 2 dollars
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Answer:
Each pizza slice costs $3
Each cola costs $2
Answer by josgarithmetic(39625) (Show Source):
You can put this solution on YOUR website! ------------------------------------------------------------------
The Harnapps order 3 slices of pizza and 3 colas and have a bill that totals $15. The Curies order 4 slices of pizza and 3 colas and have a bill that totals $18.
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p price of pizza slice
c price of cola drink
To account for each purchase sale,
You should be able to see the difference already between the two equations. Left members are almost the same; just one more p in the second equation. p is 3 dollars.
If you really need or want,
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