Question

Max is starting a tropical soda stand. Empty bottles cost $0.32 each and ingredients cost $0.10 per bottle. Additionally, Max spent $54 on a bottle-cap sealer. He will sell his soda for $1.50 per bottle.

How many bottles of soda must Max sell for his sales to equal his expenses?

FAST

Answer 1

Answer:

50 bottles of soda

Explanation:

Let "n" be the number of bottles of soda Max sells.

If empty bottles cost $0.32 each, and ingredients cost $0.10 per bottle, then the cost per bottle is $0.42. This can be expressed as 0.42n.

Max spent $54 on a bottle-cap sealer, so we add this one-off expense to the cost per bottle to give the expression for his total expenses, which is 0.42n + 54.

Max sells his soda for $1.50 per bottle. Therefore, his total revenue can be expressed as 1.5n.

To break even, Max's total revenue must equal his total expenses. So, we can set up the equation:

Solve for n:

Therefore, Max must sell 50 bottles of soda for his sales to equal his expenses.

Explanation:

Answer 2

50 bottles of soda

Explanation:

Let "n" be the number of bottles of soda Max sells.

If empty bottles cost $0.32 each, and ingredients cost $0.10 per bottle, then the cost per bottle is $0.42. This can be expressed as 0.42n.

Max spent $54 on a bottle-cap sealer, so we add this one-off expense to the cost per bottle to give the expression for his total expenses, which is 0.42n + 54.

Max sells his soda for $1.50 per bottle. Therefore, his total revenue can be expressed as 1.5n.

To break even, Max's total revenue must equal his total expenses. So, we can set up the equation:

`\begin{aligned}\sf Total \;revenue &= \sf Total \;expenses\\1.5n &= 0.42n + 54\end{aligned}`

Solve for n:

`\begin{aligned}1.5n&=0.42n+54\\1.5n - 0.42n &= 0.42n + 54 - 0.42n\\1.08n &= 54\\1.08n / 1.08 &= 54 / 1.08\\n &= 50\end{aligned}`

Therefore, Max must sell 50 bottles of soda for his sales to equal his expenses.