3. Solving Word Problems

Find the unknown numbers.

One number is nine less than another. Their sum is negative twenty-seven.

Find the unknown number.

If half of a number is added to $\frac{2}{5}$, the result is the same as subtracting $\frac{1}{10}$ from the number.

Patricia has $30$ meters of fencing to make a rectangular garden in her backyard. She wants the length to be $5$ meters more than the width. Complete steps of the word problem solving process to set up an equation Patricia could use to find the width of her rectangular fence.

Jordan is designing a picture frame for a poster. The perimeter of the frame is $80\mathrm{cm}$. The length is $12\mathrm{cm}$ longer than its width. Identify the dimensions of this poster.