Question

At the football game they sold $4 pizzas and $2 sodas which made the school$260 the number of Sodas sold was five more than three times a number of pizzas sold determine the amount of pizza and sodad sold

Answer 1

$\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}$

$\Huge \textsf{Step-by-step explanation}$

$\LARGE \bold{\textsf{Step 1: Assign Variables}}$

$\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}$

$\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}$

$\large \bold{ \textsf{From the problem, we know that:}}$

$\bullet \textsf{The school made \ 260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}$

$\large \bold{ \textsf{We can use this information to write two equations:}}$

$\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \ 4 and each soda costs \ 2)}$

$\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}$

$\LARGE \bold{\textsf{Step 3: Solve the system of equations}}$

$\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}$

$\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}$

$\large \textsf{Simplifying this expression gives us:}$

$\textsf{10\textit{p} + 10 = 260}$

$\large \textsf{Subtracting 10 from both sides:}$

$\textsf{10\textit{p} = 250}$

$\large \textsf{Dividing both sides by 10}$

$\textsf{\textit{p} = 25}$

$\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}$

$\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}$

$\large \textsf{So, 25 pizzas and 80 sodas were sold.}$

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