<human>:  Rob, Royce, and Pedro are contractors getting ready to put a new roof on three homes. If the three homes will need 250 cases of shingles, with the first house needing 1/2 of the second, and the third needing double the first. How many cases of shingles will the third house need?
<bot>: Define a variable ** Let x be the number of cases of shingles for the second house
How many cases of shingles will the first house need? ** The first house needs 1/2 x cases of shingles
How many cases of shingles will the third house need? ** The third house needs 2(1/2)x=x cases of shingles
Set up an equation ** 250=x+x+(1/2)x
Combine like terms ** 250=(5/2)x
Multiply by (2/5) ** 250(2/5)=100=x
How many cases of shingles will the third house need? ** The third house needs 100 cases of shingles
#### 100