Can the carpenter buy twelve 2-by-8 boards and fourteen 4-by-4 boards? Explain.
Understand the Problem
The question is asking if a carpenter can purchase a specified number of two types of boards without exceeding a budget of $250. We need to assess the total cost based on the given inequality and the quantities to determine if the carpenter's purchase is feasible.
Answer
No, the carpenter cannot buy twelve 2-by-8 boards and fourteen 4-by-4 boards.
Answer for screen readers
No, the carpenter cannot buy twelve 2-by-8 boards and fourteen 4-by-4 boards.
Steps to Solve
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Define the Variables Let ( x ) be the number of 2-by-8 boards and ( y ) be the number of 4-by-4 boards. According to the problem, we want to check the combination ( x = 12 ) and ( y = 14 ).
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Substitute into the Inequality We substitute the values of ( x ) and ( y ) into the inequality: $$ 8x + 12y \leq 250 $$
This translates to: $$ 8(12) + 12(14) \leq 250 $$ -
Calculate Each Term Calculate each part of the equation:
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For the 2-by-8 boards: $$ 8(12) = 96 $$
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For the 4-by-4 boards: $$ 12(14) = 168 $$
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Add the Results Now, add these two results: $$ 96 + 168 = 264 $$
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Evaluate the Inequality Now, check if the sum is within the budget: $$ 264 \leq 250 $$
This statement is false. -
Conclusion Since the sum exceeds the budget, the answer is No, the carpenter cannot buy twelve 2-by-8 boards and fourteen 4-by-4 boards.
No, the carpenter cannot buy twelve 2-by-8 boards and fourteen 4-by-4 boards.
More Information
The calculations show that the total cost for the specified number of boards is $264, which exceeds the maximum budget of $250. Understanding inequalities and proper substitution are key in solving budget-related problems.
Tips
- Not properly substituting values into the inequality.
- Forgetting to follow the order of operations when calculating the total cost.
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