max is starting a tropical soda stand. empty bottles cost $0.32 each and ingredients cost $0.10 per bottle…
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? bottles
Answer
Explanation:
Step1: Calculate cost per bottle
The cost per bottle is the sum of the cost of the empty - bottle and the cost of ingredients. So, $0.32 + 0.10=0.42$ dollars per bottle.
Step2: Set up the cost and revenue equations
Let $x$ be the number of bottles sold. The total cost $C$ is the cost of the sealer plus the cost per bottle times the number of bottles, so $C = 54+0.42x$. The total revenue $R$ is the selling - price per bottle times the number of bottles, so $R = 1.50x$.
Step3: Set cost equal to revenue and solve for $x$
Set $C = R$: [ \begin{align*} 54+0.42x&=1.50x\ 54&=1.50x - 0.42x\ 54&=1.08x\ x&=\frac{54}{1.08}\ x& = 50 \end{align*} ]
Answer:
50