Question

10 of 25Jackie and Ruth both studied very hard for their history test. Ruth studied 2 hours less than twice as many hours as Jackie.Together,"heir study time was 10 hours. How many hours did Ruth study for her history test?

Answer 1

Answer: 6 hours

Step-by-step explanation:

We have that "Ruth studied 2 hours less than twice as many hours as Jackie". I will call the hours that Ruth studied "R" and the hours that Jackie studied "J". The first equation is as follows:

`R=2J-2`

The hours that Ruth studied as 2 less than twice as many as Jackie. This will be referred to as equation 1.

Now, we are told that "Together, their study time was 10 hours" so we have the following equation:

`R+J=10`

This will be our equation 2.

The next step is to substitute equation 1 into equation 2:

`2J-2+J=10`

And we solve for J.

Combining like terms:

`3J-2=10`

We add +2 on both sides of the equation to cancel the -2 on the left side:

`\begin{gathered} 3J-2+2=10+2 \\ 3J=12 \end{gathered}`

And we divide both sides by 3:

`\begin{gathered} (3J)/(3)=(12)/(3) \\ \\ J=4 \end{gathered}`

Jackie studied for 4 hours.

Since we are asked for Ruth, we substitute J=4 into the equation 1:

`\begin{gathered} R=2J-2 \\ R=2(4)-2 \\ R=8-2 \\ R=6 \end{gathered}`

Ruth studied for 6 hours.