A juice stand sells small and large smoothies. On a certain afternoon, the stand sold a total of 180 smoothies, and the total sales from these smoothies were $900. Each small smoothie costs $4 and each large smoothie costs $6.
How many small smoothies were sold that afternoon?
For systems-of-equations word problems, first define clear variables (like for small and for large), then write one equation from the total count and another from the total value or cost. Use substitution or elimination—whichever looks simpler—to reduce to a single-variable equation, solve it carefully, and always plug back into both original conditions to quickly verify that your solution satisfies both the total number and total money constraints.
Hints
Translate words into variables
Try assigning a variable to the number of small smoothies and another variable to the number of large smoothies. What should each variable represent?
Set up two equations
One equation should come from the total number of smoothies (180), and the other from the total money collected ($900) using the $4 and $6 prices.
Reduce to one variable
From the total-number equation, solve for one variable (for example, in terms of ) and substitute into the money equation so that you have only one variable to solve for.
Check your solution
After you solve for the number of small smoothies, use it to find the number of large smoothies and verify that both the total count is 180 and the total money is $900.
Desmos Guide
Enter variables and first equation
Treat as the number of small smoothies and as the number of large smoothies. In Desmos, enter the first equation: x + y = 180.
Enter the money equation
In a new line, enter the second equation: 4x + 6y = 900.
Find the intersection point
Desmos will show two lines. Tap on their intersection point; the x-coordinate of this point is the number of small smoothies, and the y-coordinate is the number of large smoothies.
Step-by-step Explanation
Define variables
Let:
- = number of small smoothies
- = number of large smoothies
We are asked to find .
Write equations from the information
Use the two facts given:
- Total number of smoothies is 180:
- Total money is $900, with small at $4 and large at $6 each:
Now we have a system of two equations in and .
Use substitution to get one equation in one variable
From the first equation, solve for :
Substitute this into the money equation:
This equation now has only .
Solve for the number of small smoothies
Distribute and simplify:
So the number of small smoothies sold is .