Question 4·Easy·Linear Equations in One Variable
Marisol made a profit of $50 from her lemonade stand after subtracting the $8 she spent on supplies. She sold 29 cups of lemonade, each at the same price. What was the price, in dollars, of one cup of lemonade?
For SAT word problems involving profit, translate the words into simple equations using clear definitions: total sales (revenue) = price per item × number of items, and profit = total sales − cost. First compute total sales by adding profit and cost, then divide by the number of items to get the price per item. Always check that your final answer’s size and units (like dollars per cup) make sense in the context of the problem.
Hints
Relate profit, cost, and total sales
Profit is what you have left after subtracting costs from total sales. If Marisol’s profit is $50 and she spent $8 on supplies, how much money did she receive in total from customers?
Use the number of cups sold
Once you know the total amount of money from sales, think about how to use the fact that she sold 29 cups, all at the same price. What operation connects total money and number of cups to find the price of one cup?
Write and solve a simple equation
Let be the price of one cup. Write an equation using , , and the total amount of sales you found. Then solve this equation for .
Desmos Guide
Compute the price per cup
In a Desmos expression line, type (50 + 8) / 29 and look at the numerical result Desmos gives; that value is the price, in dollars, of one cup of lemonade.
Step-by-step Explanation
Find the total money from sales
Profit is what is left after subtracting costs from the total sales (revenue).
Marisol’s profit is $50 after subtracting the $8 she spent on supplies. That means her total sales must have been the profit plus the cost:
So Marisol took in $58 from selling lemonade.
Express the price per cup
She sold 29 cups of lemonade, each at the same price. Let the price of one cup be dollars.
Then:
To get , divide both sides by 29:
Now we just need to simplify this fraction.
Simplify to get the price
Simplify the fraction:
Since , we have:
So the price of one cup of lemonade was dollars.