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{`

`\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{`

`\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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