Question
Bob is building birdhouses in shop class, and he has a total of 295 nails on hand. A small birdhouse requires 24 nails and a large birdhouse requires 44 nails.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of small birdhouses
y = the number of large birdhouses
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of small birdhouses
y = the number of large birdhouses
Answers
GPT-4o mini
To express the situation as an inequality in standard form, we start by identifying the variables and the relationship between them and the total number of nails Bob has.
Let:
- \( x \) = the number of small birdhouses
- \( y \) = the number of large birdhouses
Each small birdhouse requires 24 nails, so the total number of nails used for \( x \) small birdhouses is \( 24x \). Each large birdhouse requires 44 nails, so the total number of nails used for \( y \) large birdhouses is \( 44y \).
Since Bob has a total of 295 nails, the inequality that describes this situation is:
\[
24x + 44y \leq 295
\]
This represents the constraint on the total number of nails used for both small and large birdhouses. To write it in standard form (which typically has the variables on the left side and the constant on the right side), we can rearrange it to:
\[
24x + 44y - 295 \leq 0
\]
But the original inequality \( 24x + 44y \leq 295 \) is already typically considered the standard form for representing the constraints in linear inequalities.
Let:
- \( x \) = the number of small birdhouses
- \( y \) = the number of large birdhouses
Each small birdhouse requires 24 nails, so the total number of nails used for \( x \) small birdhouses is \( 24x \). Each large birdhouse requires 44 nails, so the total number of nails used for \( y \) large birdhouses is \( 44y \).
Since Bob has a total of 295 nails, the inequality that describes this situation is:
\[
24x + 44y \leq 295
\]
This represents the constraint on the total number of nails used for both small and large birdhouses. To write it in standard form (which typically has the variables on the left side and the constant on the right side), we can rearrange it to:
\[
24x + 44y - 295 \leq 0
\]
But the original inequality \( 24x + 44y \leq 295 \) is already typically considered the standard form for representing the constraints in linear inequalities.