Tristan is selling plastic and wooden picture frames. He sells 7 frames total. The number of plastic frames Tristan sells is 5 less than twice the number of wooden frames. How many... Tristan is selling plastic and wooden picture frames. He sells 7 frames total. The number of plastic frames Tristan sells is 5 less than twice the number of wooden frames. How many of each type of frame does Tristan sell?
Understand the Problem
We need to determine how many wooden frames and plastic frames Tristan sells, given that he sells 7 frames in total and the number of plastic frames he sells is 5 less than twice the number of wooden frames.
Answer
Wooden frames: 4 Plastic frames: 3
Answer for screen readers
Wooden frames: 4 Plastic frames: 3
Steps to Solve
- Define variables
Let $x$ be the number of wooden frames and $y$ be the number of plastic frames.
- Formulate the equations
We have two pieces of information:
- Tristan sells 7 frames total: This gives us the equation $x + y = 7$.
- The number of plastic frames is 5 less than twice the number of wooden frames: This translates to $y = 2x - 5$.
- Solve the system of equations
We can use substitution to solve the system. Substitute the second equation into the first: $x + (2x - 5) = 7$
- Simplify and solve for x
Combine like terms: $3x - 5 = 7$ Add 5 to both sides: $3x = 12$ Divide by 3: $x = 4$
- Solve for y
Substitute $x = 4$ into either equation. Using the first equation: $4 + y = 7$ Subtract 4 from both sides: $y = 3$
- State the solution
Tristan sells 4 wooden frames and 3 plastic frames.
Wooden frames: 4 Plastic frames: 3
More Information
The solution indicates that Tristan sells 4 wooden frames and 3 plastic frames. This satisfies both conditions given in the problem.
Tips
A common mistake would be misinterpreting the phrase "5 less than twice the number of wooden frames" and writing the equation as $y = 5 - 2x$ instead of $y = 2x - 5$.
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