A rental car company charges $63.25 per day to rent a car and $0.07 for every mile driven. Ella wants to rent a car, knowing that:
She plans to drive 50 miles.
She has at most $130 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Ella can afford to rent while staying within her budget.
Answer
Attempt 1 out of 2
Inequality:
63.25x + 0.07(50)x ≤ 130
Explanation:
The total cost for x number of days can be represented as 63.25x (the cost per day multiplied by the number of days) plus 0.07(50)x (the cost per mile multiplied by the number of miles driven). This total cost must be less than or equal to $130, which is Ella's budget.
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Apologies for the confusion. Let me clarify the inequality.
The cost per day to rent a car is $63.25. The cost per mile driven is $0.07. The total cost can be calculated as (63.25 * x) + (0.07 * 50), where x is the number of days Ella plans to rent the car.
We have to ensure that the total cost (63.25 * x) + (0.07 * 50 * x) does not exceed $130.
Therefore, the inequality is:
(63.25 * x) + (0.07 * 50 * x) ≤ 130
Simplifying the equation:
63.25x + 3.5x ≤ 130
Combining like terms:
66.75x ≤ 130
To solve for x, divide both sides of the inequality by 66.75:
x ≤ 130 / 66.75
So, Ella can afford to rent the car for at most approximately 1.95 days. Since she cannot rent for a fraction of a day, she can afford to rent the car for 1 day.
Violet needs to order some new supplies for the restaurant where she works. The restaurant needs at least 800 glasses. There are currently 164 glasses. If each set on sale contains 6 glasses, write and solve an inequality which can be used to determine xx, the number of sets of glasses Violet could buy for the restaurant to have enough glasses.
Answer
Attempt 1 out of 2
Inequality:
xx
Let xx be the number of sets of glasses Violet could buy.
To find the total number of glasses she can buy, we need to multiply the number of sets by the number of glasses in each set.
Since each set contains 6 glasses, the total number of glasses Violet can buy is 6x.
To ensure that the restaurant has at least 800 glasses, we set up the following inequality:
164 + 6x ≥ 800
Simplifying the inequality:
6x ≥ 800 - 164
6x ≥ 636
Dividing both sides of the inequality by 6:
x ≥ 636 / 6
x ≥ 106
Therefore, Violet can buy at least 106 sets of glasses for the restaurant to have enough glasses.
Owen has a points card for a movie theater.
He receives 30 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 115 points for a free movie ticket.
Write and solve an inequality which can be used to determine xx, the number of visits Owen can make to earn his first free movie ticket.
Answer
Attempt 1 out of 2
Inequality:
xx
Let xx be the number of visits Owen can make to earn his first free movie ticket.
Owen receives 30 points just for signing up and earns 12.5 points for each visit to the movie theater. Therefore, the total number of points he can earn after xx visits can be represented as 30 + 12.5x.
To earn a free movie ticket, Owen needs at least 115 points. So we can set up the following inequality:
30 + 12.5x ≥ 115
Subtracting 30 from both sides of the inequality:
12.5x ≥ 115 - 30
12.5x ≥ 85
Dividing both sides of the inequality by 12.5:
x ≥ 85 / 12.5
x ≥ 6.8
Therefore, Owen can make at least 6 visits to earn his first free movie ticket. Since he cannot make a fraction of a visit, Owen will need to make at least 7 visits to earn his first free movie ticket.
Select the values that make the inequality x/-4≥-9
≥−9 true. Then write an equivalent inequality, in terms of xx.
(Numbers written in order from least to greatest going across.)
Answer
Attempt 1 out of 2
28 32 33
35 36 37
39 40 44
Equivalent Inequality: xx
To find the values that make the inequality x/-4 ≥ -9 true, we can solve the inequality:
x/-4 ≥ -9
Multiplying both sides of the inequality by -4 (since we want to isolate x), we need to reverse the inequality sign:
x ≤ -9 * -4
x ≤ 36
Therefore, any value of x that is less than or equal to 36 will make the inequality x/-4 ≥ -9 true.
The equivalent inequality in terms of x is:
x ≤ 36
28 32 33
35 36 37
39 40 44