Question

In Exercises 67 and 68 , use the following information. In every square inch of sailcloth, the warp (lengthwise threads) intersects the weft (crosswise threads) about 9000 times. The density (number of threads per inch) of the weft threads to the warp threads is about 5 to 2. Write an equation that you can solve to find the number of threads per square inch. Let \(x\) represent the number of warp threads.

Short answer

The equation that can be used to find the number of threads per square inch is \(5x + 2x = 9000\), with \(x\) representing the number of warp threads.

Step-by-step solution

Identify the given information

From the problem, we know that the warp intersects the weft about 9000 times per square inch and the density ratio of weft to warp is 5 to 2.

Formulate the ratio into an equation

Using the given ratio, we can write an equation saying that the number of weft threads (\(5x\)) to the warp threads (\(2x\)) equals the total intersection points.

Write the final equation

So, the final equation becomes \(5x + 2x = 9000\) where \(x\) represents the number of warp threads.