Select the correct answer.
Naomi can spend up to $18.00 for a trip to the bowling alley. The cost per game is $3.25, and shoe rental for the day is $1.50. Which inequality can be used to solve for $x$, the number of games that Naomi can bowl?
A. $1.50 x+3.25 \geq 18.00$
B. $1.50 x+3.25 \leq 18.00$
C. $3.25 x+1.50 \geq 18.00$
D. $3.25 x+1.50 \leq 18.00
Answer (2)
Define x as the number of games Naomi can bowl.
Express the total cost as 3.25 x + 1.50 .
Set up the inequality 3.25 x + 1.50 ≤ 18.00 .
The correct answer is 3.25 x + 1.50 ≤ 18.00 , which is not explicitly listed in the options. However, the closest representation of the situation is 3.25 x + 1.50 ≤ 18.00 .
Explanation
Problem Analysis Let's analyze the problem. Naomi has a budget of $18.00 for her trip to the bowling alley. The cost per game is $3.25 , and the shoe rental is $1.50 . We need to find the inequality that represents the number of games, x , that Naomi can bowl.
Formulating the Inequality The cost of bowling x games is 3.25 x . The total cost of the trip is the cost of the games plus the shoe rental, which is 3.25 x + 1.50 . Since Naomi can spend up to $18.00 , the total cost must be less than or equal to $18.00 . Therefore, the inequality is: 3.25 x + 1.50 ≤ 18.00
Comparing with Options Now, let's compare this inequality with the given options:
A. 1.50 x + 3.25 ≥ 18.00 (Incorrect: This reverses the costs and the inequality sign.)
B. 150 x + 3.25 ≤ 1800 (Incorrect: This seems to be multiplying x by 100 for some reason.)
C. 3.25 x + 1.50 ≥ 18.00 (Incorrect: This implies Naomi can spend more than $18.00 .)
D. 325 x + 150 = 18.00 (Incorrect: This is an equation, not an inequality, and it multiplies x and the constant by 100.)
The correct inequality is 3.25 x + 1.50 ≤ 18.00 , which is not explicitly listed. However, we can manipulate the inequality to match one of the options. Multiplying both sides of the inequality by 100, we get: 100 ( 3.25 x + 1.50 ) ≤ 100 ( 18.00 ) 325 x + 150 ≤ 1800
However, this is still not one of the options. The correct inequality representing the situation is 3.25 x + 1.50 ≤ 18.00 .
Finding the Correct Option The inequality that represents the given situation is 3.25 x + 1.50 ≤ 18.00 . None of the options match this inequality exactly. However, if we look closely, option B is 1.50 x + 3.25 ≤ 18.00 , which is not correct. The correct inequality should be 3.25 x + 1.50 ≤ 18.00 .
Final Answer Let's re-examine the options. We are looking for 3.25 x + 1.50 ≤ 18.00 . Option B is 1.50 x + 3.25 ≤ 18.00 , which is not correct. However, if we consider the original problem statement, we are looking for the inequality that can be used to solve for x . The correct inequality is 3.25 x + 1.50 ≤ 18.00 .
Conclusion The correct inequality is 3.25 x + 1.50 ≤ 18.00 . However, none of the options match this inequality exactly. It seems there might be a typo in the options. The closest option is B if we assume the decimal points were misplaced, but even then, the terms are reversed. Therefore, we will choose the option that best represents the situation, which is 3.25 x + 1.50 ≤ 18.00 .
Examples
Imagine you're planning a party and have a budget. Each item costs a certain amount, and you need to figure out how many of each item you can buy without exceeding your budget. This problem is similar to figuring out how many games Naomi can bowl. Understanding inequalities helps you manage your finances and make informed decisions about spending.
The inequality that represents how many games Naomi can bowl is 3.25 x + 1.50 \teq 18.00 . Among the options provided, the correct choice is Option D: 3.25 x + 1.50 \teq 18.00 . This inequality correctly indicates that the total cost, including game costs and shoe rental, must not exceed her $18.00 budget.
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