County carpets charges $22 per square yard for carpeting, and an additional installation fee of $100. city carpets charges $25 per square yard for the same carpeting, and an additional installation fee of $70. write and solve an equation to find the number of square yards of carpeting for which the total cost charges by the two companies will be the same.

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

Beth makes batches of bluberry muffins and banna muffins. each batchis 6 muffins. she makes 2.5 batches of bluberry muffins. how many batches of bananna muffins should beth make if she wants to have a total of 60 muffins?

Show your workcan a right triangle have this sides? *how to prove it without using the pythagorean theorema*