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:

Question

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

Answer 1

Let's solve the equation step by step.

The equation given is:

\[ 300x + \frac{500}{7}y = 10,000 \]

You've mentioned \( y = 87.5 \). We can substitute that into the equation:

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

Next, calculate \( \frac{500}{7} \times 87.5 \):

\[ \frac{500 \times 87.5}{7} = \frac{43750}{7} \approx 6250 \]

Now substitute this value back into the equation:

\[ 300x + 6250 = 10,000 \]

Next, isolate \( 300x \):

\[ 300x = 10,000 - 6250 \] \[ 300x = 3750 \]

Now, solve for \( x \):

\[ x = \frac{3750}{300} = 12.5 \]

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

\[ \boxed{12.5} \]