Answer:
The Smith generates 6 bags of trash per month, and the Joneses generates 6 bags of trash per month.
Step-by-step explanation:
We know that
- The Smith generates one and a half times trash as much as the Joneses.
- Both families generate 15 bags of trash per month.
To solve this problem, we need to transform each statement in a equation.
\(S=1\frac{1}{2}J\)
Where \(S\) represents the Smith, and \(J\) represents the Joneses.
This expressions expresses the one and a half difference between the two families.
If both families produce 15 bags of trash, the equation would be
\(S+J=15\)
Now, we replace the first equation into the second one and solve for \(J\)
\(1\frac{1}{2}J+J=15\\1.5J+J=15\\2.5J=15\\J=\frac{15}{2.5}=6\)
Then, we replace this value into one equation to find the other variable
\(S+J=15\\S+6=15\\S=15-6\\S=9\)
Therefore, the Smith generates 6 bags of trash per month, and the Joneses generates 6 bags of trash per month.
