Answer:
290n + 120 ≤ 1400
4 days
Step-by-step explanation:
Given that:
Vacation budget = $1400
Cost on hotel = $110 per night
Cost on food = $80 per day
Cost on activities = $100 per day
Cost on gas = $120 for entire trip
Number of nights they can afford to stay
Let the Number of nights they can afford = n
((110 + 80 + 100) * number of nights) + 120 ≤ vacation budget
290n + 120 ≤ 1400
290n ≤ 1400 - 120
290n ≤ 1280
n ≤ 1280 / 290
n ≤ 4.4137
Hence, longest vacation they can take is 4 days
The family can afford up to 4 nights for their vacation, as per the inequality 290n + 120 ≤ 1400, where 'n' stands for the number of nights.
Let's first define the total expenses per day as the sum of the hotel costs ($110), food costs ($80), and the daily amount for activities ($100). This adds up to $290 per day. So for 'n' nights, the family will be spending $290n. In addition, there's a $120 onetime expense for gasoline. Hence, the inequality representing their spending will be: 290n + 120 ≤ 1400.
To find the longest vacation this family can afford, we simply need to solve this inequality. Pay attention as we do this: 290n ≤ 1280 (subtracting 120 from both sides), and then n ≤ 4.41 (dividing both sides by 290).
Since the number of nights 'n' should be a whole number, the family can afford up to 4 nights on their vacation.
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Answer:
1- 58
2- 70
3- 125
4- 93
Step-by-step explanation:
Enter the least whole number of hours the student needs to work in order to earn at least $200
Answer: 7.50 h ≥200
She needs to work 27 hours to earn at least $200.
Step-by-step explanation:
Hi, to write the inequality we have to analyze the information given:
So, she earns $7.50 per hour, the expression that represents the statement is $7.50h.
She wants to earn at least $200, "at least" means more or equal (≥200).
Mathematically speaking:
This is the inequality that represents all of the possible numbers of hours (h) the student could work to meet her goal.
For the second part we simply solve the inequation:
7.50 h ≥200
h ≥200/7.50
h ≥ 26.67
Rounded to the nearest whole number:
h ≥ 27
She needs to work 27 hours to earn at least $200.
Answer:
3; all real numbers except x=2
0.75
(6 + 4)n = 18
4n + 18 = 6
6 + 4n = 18
6 + 4 + n = 18
The correct mathematical equation for the statement is 6 + 4n = 18
Given data:
The correct translation of the statement "Six, plus four times a number, is eighteen" into a mathematical equation is:
6 + 4n = 18
In the equation, "n" represents the unknown number.
The statement states that the sum of six and four times the number is equal to eighteen.
The expression "4n" represents four times the number, and adding 6 to it gives the total of eighteen.
Hence, the expression is 6 + 4n = 18.
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