To find the year when the number of men and women receiving bachelor's degrees are equal, we can use the equations given:
For men:
\[ y = 3.9x + 443 \]
For women:
\[ y = 14.3x + 316 \]
To find the point where the number of men and women receiving degrees are the same, we can set the two equations equal to each other:
\[ 3.9x + 443 = 14.3x + 316 \]
Now, let's solve for \( x \):
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Subtract \( 3.9x \) from both sides: \[ 443 = 14.3x - 3.9x + 316 \] \[ 443 = 10.4x + 316 \]
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Subtract \( 316 \) from both sides: \[ 443 - 316 = 10.4x \] \[ 127 = 10.4x \]
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Divide both sides by \( 10.4 \): \[ x = \frac{127}{10.4} \] \[ x \approx 12.19 \]
Since \( x \) represents the number of years after 1970, we can find the year: \[ 1970 + 12.19 \approx 1982.19 \]
This suggests that in the year approximately around 1982, the number of bachelor's degrees awarded to men and women were equal.
Next, we can substitute \( x \) back into either equation to find \( y \):
Let's use the men's equation: \[ y = 3.9(12.19) + 443 \] \[ y \approx 47.6 + 443 \] \[ y \approx 490.6 \]
Thus, the ordered pair where the number of degrees awarded to men and women is equal is approximately: \[ (1982, 490.6) \]
To recap, the degree awards become equal around the year 1982 with approximately 490,600 degrees awarded.
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