a drama club is panning a bus trip to New York City to see a broadway play. The cost per person for the bus rental varies inversely as the number of people going on the trip. It will cost $30 per person if 44 people go on the trip. How much will it cost if 55 people go on the trip? Round your answer to the nearest cent, if necessary.
Let x be the cost per person if 55 people go on the trip. Then, we know that:
30 = k/44
where k is the constant of proportionality. We can solve for k by cross-multiplying:
30 * 44 = k
k = 1320
Now, we can use k to find x:
x = k/55
x = 1320/55
x ≈ 24
Therefore, it will cost approximately $24 per person if 55 people go on the trip.
are your sure
Yes, the answer is correct. If you take the cost per person as $24 and multiply it by 55 (number of people going on the trip), you will get the total cost as $1320, which is the same as the total cost when there are 44 people going on the trip at a cost of $30 per person. This confirms that the cost per person varies inversely with the number of people going on the trip.
To find out how much it will cost if 55 people go on the trip, we can set up an inverse variation equation.
Let x represent the number of people going on the trip and y represent the cost per person for the bus rental.
According to the problem, the cost per person varies inversely as the number of people going on the trip. This can be represented by the equation:
xy = k
where k is a constant.
We are given that it will cost $30 per person if 44 people go on the trip. Let's use this information to find the value of k:
44 * 30 = k
1320 = k
Now that we have the value of k, we can use it to find the cost per person if 55 people go on the trip.
55 * y = 1320
Divide both sides of the equation by 55 to isolate y:
y = 1320 / 55
y ≈ $24
Therefore, it will cost approximately $24 per person if 55 people go on the trip.
To find the cost per person if 55 people go on the trip, we can use the inverse variation equation. Inverse variation means that as the number of people increases, the cost per person decreases.
Let's denote the number of people as "x" and the cost per person as "y". According to the problem, when 44 people go on the trip, the cost per person is $30.
The inverse variation equation is given by:
y = k/x
where "k" is the constant of variation.
To find the value of "k", we can substitute the given values into the equation:
30 = k/44
To solve for "k", we can cross-multiply:
30 * 44 = k
k = 1320
Now that we have the value of "k", we can use it to find the cost per person if 55 people go on the trip:
y = 1320/55
y ≈ $24
Therefore, if 55 people go on the trip, it will cost approximately $24 per person.