Question

The smith is generate one and a half times as much as their neighbors, the joneses. Together, the two households produce 15 bags of trash each month. How much trash does each household generate ?

Answer 1

Smith = 1.5Jones
S=1.5J
S + J = 15
1.5J + J = 15
2.5J = 15
J = 6
S = 9

Answer 2

The Smith generates 6 bags of trash per month, and the Joneses generates 6 bags of trash per month.

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(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(1)/(2)J+J=15\\1.5J+J=15\\2.5J=15\\J=(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.