Question

The school has budgeted $3,500 for an end-of -year party in the local park. The cost to rent the park shelter is $250. How much can the student council spend per student on food if each of the three hundred students receives a $5.50 gift?(a) Write the equation from the given information.(b) Solve the equation showing ALL of the steps.

Answer 1

So for part a we need to build an equation. We know that the budget is $3500 and that we must discount $250 for the park shelter rent. We also need to discount the money spent on gift for the 300 students. The sum of these two expenses and the amount of money that can be spent on food must be equal to the total budget. Then we have the equation for part a:

`3500=250+300\cdot5.50+300x`

Where the x represents the money that can be spent for food per student.

Solving this equation is part b so let's start. First we perform a multiplication:

`\begin{gathered} 3500=250+300\cdot5.50+300x \\ 3500=250+1650+300x \end{gathered}`

Then, since the first two terms of the right side are constant not multiplied by x we are going to add them:

`\begin{gathered} 3500=250+1650+300x \\ 3500=1900+300x \end{gathered}`

Now we pass the 1900 to the left side as a negative number and perform the substraction:

`\begin{gathered} 3500=1900+300x \\ 3500-1900=300x \\ 1600=300x \end{gathered}`

Finally, we pass the 300 to the left side as a divider and we calculate x:

`\begin{gathered} 1600=300x \\ (1600)/(300)=x \\ 5.333=x \end{gathered}`

Which means that the student council can spend $5.333 on food per student.