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Answer :
To solve this problem, let's break it down step-by-step:
1. Understand the Situation:
- Taka bought a coat and a pair of shoes.
- The total amount Taka spent on both items is no more than [tex]$122.
2. Define Variables:
- Let \( x \) represent the cost of the coat.
- Let \( y \) represent the cost of the shoes.
3. Set Up the Inequality:
- Since the total cost of the coat and shoes should not exceed $[/tex]122, we can write the inequality:
[tex]\[
x + y \leq 122
\][/tex]
4. Solve for the Variable of Interest:
- We need to find an inequality that represents just the price of the shoes [tex]\( y \)[/tex]. To do this, solve the inequality for [tex]\( y \)[/tex]:
[tex]\[
y \leq 122 - x
\][/tex]
5. Match with the Given Options:
- Compare the expression [tex]\( y \leq 122 - x \)[/tex] with the available options:
- a) [tex]\( y \leq 122 + x \)[/tex]
- b) [tex]\( y \leq 122 - x \)[/tex]
- c) [tex]\( y - x \geq 122 \)[/tex]
- d) [tex]\( 122 \leq y + x \)[/tex]
6. Conclusion:
- The expression [tex]\( y \leq 122 - x \)[/tex] matches option b).
Therefore, the inequality that best represents the price of the shoes is:
[tex]\[ \text{Option b: } y \leq 122 - x \][/tex]
1. Understand the Situation:
- Taka bought a coat and a pair of shoes.
- The total amount Taka spent on both items is no more than [tex]$122.
2. Define Variables:
- Let \( x \) represent the cost of the coat.
- Let \( y \) represent the cost of the shoes.
3. Set Up the Inequality:
- Since the total cost of the coat and shoes should not exceed $[/tex]122, we can write the inequality:
[tex]\[
x + y \leq 122
\][/tex]
4. Solve for the Variable of Interest:
- We need to find an inequality that represents just the price of the shoes [tex]\( y \)[/tex]. To do this, solve the inequality for [tex]\( y \)[/tex]:
[tex]\[
y \leq 122 - x
\][/tex]
5. Match with the Given Options:
- Compare the expression [tex]\( y \leq 122 - x \)[/tex] with the available options:
- a) [tex]\( y \leq 122 + x \)[/tex]
- b) [tex]\( y \leq 122 - x \)[/tex]
- c) [tex]\( y - x \geq 122 \)[/tex]
- d) [tex]\( 122 \leq y + x \)[/tex]
6. Conclusion:
- The expression [tex]\( y \leq 122 - x \)[/tex] matches option b).
Therefore, the inequality that best represents the price of the shoes is:
[tex]\[ \text{Option b: } y \leq 122 - x \][/tex]
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