Question

question christian and his children went into a movie theater and he bought $59.75 worth of bags of popcorn and candies. each bag of popcorn costs $5 and each candy costs $3.25. he bought a total of 13 bags of popcorn and candies altogether. determine the number of bags of popcorn and the number of candies that christian bought. answer attempt 1 out of 2 christian bought bags of popcorn and candies.

Explanation:

Step1: Set up equations

Let $x$ be the number of bags of popcorn and $y$ be the number of candies. We have two - equations: $x + y=13$ (total number of items) and $5x + 3.25y=59.75$ (total cost). From $x + y=13$, we can get $x = 13 - y$.

Step2: Substitute into cost - equation

Substitute $x = 13 - y$ into $5x+3.25y = 59.75$. So $5(13 - y)+3.25y=59.75$. Expand the left - hand side: $65-5y + 3.25y=59.75$.

Step3: Combine like terms

Combine the $y$ terms: $65-(5y - 3.25y)=59.75$, which simplifies to $65 - 1.75y=59.75$.

Step4: Solve for $y$

Subtract 65 from both sides: $-1.75y=59.75 - 65=-5.25$. Then divide both sides by $-1.75$: $y=\frac{-5.25}{-1.75}=3$.

Step5: Solve for $x$

Since $x = 13 - y$ and $y = 3$, then $x=13 - 3 = 10$.

Answer:

Christian bought 10 bags of popcorn and 3 candies.