Question

use the multiplication equality to solve for the unknown. A video game system and several games are sold for 632.dollar . The cost of the games is 3 times as much as the cost of the system. Find the cost of the system and the cost of the game

Answer 1

The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.

We have that the videogame system and games cost $632. And the cost of the games is 3 times as much as the cost of the system. Then we have the following expressions:

`\begin{gathered} VS+G=632 \\ G=3\cdot VS \end{gathered}`

Where, VS = Videogame system and G = games.

We plug in 3*VS in the first equation to get:

`VS+3\cdot VS=632`

And we solve for VS, to find the cost of the videogame system:

`4\cdot VS=632`

We use the multiplication property of equality here, and multiply both sides of the equation by 1/4:

`\begin{gathered} 4\cdot VS\cdot(1)/(4)=632\cdot(1)/(4) \\ VS=158 \end{gathered}`

The cost of the videogame system is $158. Now we can find the cost of the games, replacing VS in the first equation:

`\begin{gathered} VS+G=632 \\ 158+G=632 \\ G=632-158=474 \end{gathered}`

Games cost $474.