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Chapter 7 of the Jiuzhang suanshu presents a problem of two linear equations involving acres of land and their respective prices. One of the two equations can be translated to:

300x + 300 x plus StartFraction 500 over 7 EndFraction left-parenthesis 87.5 right-parenthesis equals 10,000.y = 10000
If y = 87.5, what is the value for x?

300x + 300 x plus StartFraction 500 over 7 EndFraction y equals 10,000.y = 10,000

300x + 300 x plus StartFraction 500 Over 7 EndFraction y equals 10,000.(87.5) = 10,000
300x + 6,250 = 10,000
x =

1 answer

To solve for \( x \) given the equation

\[ 300x + 300x + \frac{500}{7}(87.5) = 10,000, \]

we need to first simplify the equation.

  1. Combine the terms involving \( x \):

\[ 300x + 300x = 600x. \]

So now we have:

\[ 600x + \frac{500}{7}(87.5) = 10,000. \]

  1. Next, let's calculate \( \frac{500}{7}(87.5) \):

\[ \frac{500}{7}(87.5) = \frac{500 \times 87.5}{7} = \frac{43,750}{7} \approx 6,250. \]

So, we replace \( \frac{500}{7}(87.5) \) with \( 6,250 \) in the equation:

\[ 600x + 6,250 = 10,000. \]

  1. Now we isolate \( x \):

Subtract \( 6,250 \) from both sides:

\[ 600x = 10,000 - 6,250, \]

\[ 600x = 3,750. \]

  1. Finally, divide both sides by \( 600 \) to solve for \( x \):

\[ x = \frac{3,750}{600} = 6.25. \]

Thus, the value of \( x \) is:

\[ \boxed{6.25}. \]