Jane cuts a piece of twine into three pieces. The second pieces is 7 times as long as the

first piece, and the third piece is 5 feet

longer than the first piece. If the total

length of the twine is 320 feet, find the

lengths of each of the three pieces.

Twine into three pieces, lets call them x, y and z

The second piece is 7 times as long as the first piece

7x = y

The third piece is 5 feet longer than the first piece

x + 5 = z

The total length of twine is 320 feet

x + y + z = 320

This is a simultaneous equation.

My goal is to make the final equation in terms of x i. e. 5.5x = 320

I choose the final equation because it is the only equation which has a value in it.

We will substitute the first and second equation into the third equation.

7x = y, x + 5 = z

x + y + z = 320

x + (7x) + (x+5) = 320

9x + 5 = 320

9x = 315

x = 35

Now that we know x, we can substitute it into the first and second equation to find x and y

7x = y = > 7 (35) = y = > 245 = y

x + 5 = z = > (35) + 5 = z = > 40 = z

In summary

>The first piece, x, is 35 feet long

>The second piece, y, is 245 feet long

>The third piece, z, is 40 feet log