Question

(Get 30 points for answer, please answer truthfully)

Carter and his children went into a movie theater and he bought $33 worth of drinks and candies. Each drink costs $4.50 and each candy costs $3. He bought 3 times as many drinks as candies. Determine the number of drinks and the number of candies that Carter bought.

Answer 1

6 drinks

2 boxes of candy

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Step-by-step explanation:

x = number of drinks

y = number of boxes of candy

These two variables represent positive integers.

"He bought 3 times as many drinks as candies" which means we can set up the equation x = 3y

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1 drink costs $4.50

x drinks cost 4.50x dollars

1 box of candy costs $3

y boxes of candy cost 3y dollars.

4.50x + 3y = total cost = 33 dollars

Therefore, we arrive at the second equation of 4.50x+3y = 33

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We have this system of equations

`\begin{cases}x = 3y\\4.50x+3y = 33\end{cases}`

I'll use substitution to solve. Replace x with 3y in the second equation, then isolate y.

`4.50x+3y = 33\\\\4.50(3y)+3y = 33\\\\13.50y+3y = 33\\\\16.50y = 33\\\\y = 33/16.50\\\\y = 2\\\\`

This tells us he bought 2 boxes of candy.

Use that value to find x.

`x = 3y\\\\x = 3*2\\\\x = 6\\\\`

Carter also bought 6 drinks.

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Check:

• 6 drinks = 6*4.50 = 27 dollars
• 2 boxes of candy = 2*3 = 6 dollars
• Total cost = 27+6 = 33 dollars

The answers are confirmed.

Another way to confirm the answers is to plug (x,y) = (6,2) into each equation of the system I mentioned earlier. After simplifying, you should get the same thing on both sides.

A visual way to confirm the answers is to graph each equation on the same xy grid. The two lines intersect at (6,2). You can use a graphing tool such as Desmos or GeoGebra.