Can you PLEASE help me with this Algebra problem:
In a hotel conference room, the number of chairs is 47 more than the number of people currently in the room. The total number of legs currently in this room is 938. What is the sum of the digits in the number of people currently in this room? Write a system of equations for this situation and find its solution.
This is what I have so far:
x = # of chairs
Y = # of people
number of legs = 938
I am not sure how to format the equation...but should I divide 938/2 = 469 number of people?
equation #1:
x - y = 47
equation #2: deals with the number of legs
4x + 2y = 938, or
2x + y = 469
add our two equations:
3x = 516
take over....
Let's work through this step by step.
We are given:
1) The number of chairs is 47 more than the number of people currently in the room.
2) The total number of legs currently in the room is 938.
3) We need to find the sum of the digits in the number of people currently in this room.
Let's represent the number of chairs as "x" and the number of people as "y".
From the first given information, we can write an equation:
x = y + 47
Next, let's consider the number of legs in the room. Each chair has 4 legs, and each person has 2 legs. So, the total number of legs can be expressed as:
4x + 2y = 938
Now, we have a system of equations:
x = y + 47
4x + 2y = 938
To find the solution, we can use substitution or elimination method. Let's use substitution:
From equation 1, we can express x in terms of y:
x = y + 47
Substituting this value of x in equation 2:
4(y + 47) + 2y = 938
4y + 188 + 2y = 938
6y + 188 = 938
6y = 938 - 188
6y = 750
y = 750 / 6
y = 125
Now that we know y = 125, we can substitute this value back into equation 1 to find x:
x = 125 + 47
x = 172
Therefore, the number of people currently in the room is 125, and the number of chairs is 172.
Finally, we need to find the sum of the digits in the number of people currently in the room:
The sum of the digits in 125 is 1 + 2 + 5 = 8.
So, the answer to the problem is 8.