last year, 2713 teachers attended a technology conference. if there were 163 more men than women at the conference, how many men and how many women attended?
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Let w = number of women. Solve for w.
w + w + 163 = 2713
Let's denote the number of women attending the conference as "W" and the number of men attending as "M."
According to the information given, we know that the total number of teachers attending the conference is 2713. Therefore, we can set up an equation based on this information:
W + M = 2713 (Equation 1)
We are also told that there were 163 more men than women at the conference. This can be represented as:
M = W + 163 (Equation 2)
To solve this system of equations, we can substitute Equation 2 into Equation 1:
W + (W + 163) = 2713
Simplifying this equation:
2W + 163 = 2713
Subtracting 163 from both sides:
2W = 2550
Dividing both sides by 2:
W = 2550/2
W = 1275
Now, substitute the value of W back into Equation 2 to find the number of men:
M = W + 163
M = 1275 + 163
M = 1438
Therefore, there were 1275 women and 1438 men attending the technology conference.
To determine how many men and how many women attended the conference, we can set up a system of equations and solve them algebraically.
Let's represent the number of women as "x" and the number of men as "x + 163" (since there were 163 more men than women).
We know that there were a total of 2713 teachers. So, the equation would be:
x + (x + 163) = 2713
Simplifying the equation, we have:
2x + 163 = 2713
2x = 2713 - 163
2x = 2550
x = 2550 / 2
x = 1275
This tells us that there were 1275 women at the conference. To find the number of men, we substitute this value back into our equation:
x + 163 = 1275 + 163
x + 163 = 1438
Therefore, there were 1438 men at the conference.
In summary, 1275 women and 1438 men attended the technology conference.