a soda vendor sold large sodas for $3 and small sodas for $2.if he sold 182 large sodas and his gross profit for the day was $894, how many small sodas did he sell ?
convert words to equation
3L+2S=894
L=182
put that L into the first equation, and solve for S.
To convert the given information into an equation, we can assign variables to the unknowns. Let's say the number of small sodas sold is "x".
According to the given information:
Large sodas sold: 182
Price of a large soda: $3
Small sodas sold: x (unknown)
Price of a small soda: $2
Gross profit for the day: $894
Now, let's convert the words into an equation:
The total revenue from large sodas sold = Price per large soda × Number of large sodas sold
The total revenue from small sodas sold = Price per small soda × Number of small sodas sold
The total revenue from large sodas sold = 3 × 182 (since the price of a large soda is $3)
The total revenue from small sodas sold = 2 × x (since the price of a small soda is $2)
The total revenue from all soda sales = Revenue from large sodas + Revenue from small sodas
Total revenue = (3 × 182) + (2 × x)
However, the question provides us with the gross profit, not the total revenue. Gross profit is calculated by subtracting the cost of goods sold (COGS) from the total revenue.
Gross profit = Total revenue - COGS
Since we don't know the COGS, we can write:
Gross profit = (3 × 182) + (2 × x) - COGS
We are given that the gross profit for the day was $894, so:
894 = (3 × 182) + (2 × x) - COGS
Now, the COGS is equal to the cost of goods for large sodas plus the cost of goods for small sodas:
COGS = Cost per large soda × Number of large sodas sold + Cost per small soda × Number of small sodas sold
COGS = (3 × 182) + (2 × x)
Plugging this into the equation, we have:
894 = (3 × 182) + (2 × x) - [(3 × 182) + (2 × x)]
Simplifying the equation:
894 = 546 + 2x - 546 - 2x
Now, any terms involving "x" cancel out, leaving:
894 = 546 - 546
894 = 0
Since this equation is impossible, it means that there is no solution for the number of small sodas sold (x).
Therefore, based on the given information, we cannot determine how many small sodas the vendor sold.