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Answer :
To solve the problem, let's set it up step by step using the variables provided:
1. Identify the Variables:
- Let [tex]\( x \)[/tex] be the number of children.
- Let [tex]\( y \)[/tex] be the number of adults.
2. Understand the Problem:
- Each child is served 2 pancakes. Therefore, if there are [tex]\( x \)[/tex] children, they will need [tex]\( 2x \)[/tex] pancakes in total.
- Each adult is served 3 pancakes. Therefore, if there are [tex]\( y \)[/tex] adults, they will need [tex]\( 3y \)[/tex] pancakes in total.
- Together, both the children and the adults can be served up to 122 pancakes because that's the maximum number prepared by the chef.
3. Formulate the Inequality:
- The total pancakes served to both children and adults should not exceed 122. Therefore, we set up the inequality:
[tex]\[
2x + 3y \leq 122
\][/tex]
4. Select the Correct Inequality:
- Comparing with the options provided, the inequality that correctly describes this situation is:
[tex]\[
2x + 3y \leq 122
\][/tex]
This inequality ensures that the total number of pancakes served to both children and adults does not exceed the maximum number made, which is 122 pancakes.
1. Identify the Variables:
- Let [tex]\( x \)[/tex] be the number of children.
- Let [tex]\( y \)[/tex] be the number of adults.
2. Understand the Problem:
- Each child is served 2 pancakes. Therefore, if there are [tex]\( x \)[/tex] children, they will need [tex]\( 2x \)[/tex] pancakes in total.
- Each adult is served 3 pancakes. Therefore, if there are [tex]\( y \)[/tex] adults, they will need [tex]\( 3y \)[/tex] pancakes in total.
- Together, both the children and the adults can be served up to 122 pancakes because that's the maximum number prepared by the chef.
3. Formulate the Inequality:
- The total pancakes served to both children and adults should not exceed 122. Therefore, we set up the inequality:
[tex]\[
2x + 3y \leq 122
\][/tex]
4. Select the Correct Inequality:
- Comparing with the options provided, the inequality that correctly describes this situation is:
[tex]\[
2x + 3y \leq 122
\][/tex]
This inequality ensures that the total number of pancakes served to both children and adults does not exceed the maximum number made, which is 122 pancakes.
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