Question

Justice lived in Germany and Hollands for a total of 24 months in order to learn German. He learned and average of 120 words per month when he lived in Germany, and an average of 220 words per month when he lived in Holland. In total, he learned a total of 3780 new words. How long did justice live in Germany and Holland?

Answer 1

Justice lived in Germany for 15 months and he lived in Holland for 9 months.

Explanation:

1. You must make a system of equations:

`\left \{ {{x+y=24} \atop {120x+220y=3780}} \right.`

Where
`x` is the number on months he lived in Germany and
`y` is the number on months he lived in Holland.

2. You can solve this system of equations by using the Elimination Method. If you multiply the first equation by -120, you can cancel the variable
`x` when you add both equations, and then you can calculate
`y`. When you obtain the value of
`y`, you can substitute it into one of the original equations and solve for
`x`. Then:

`\left \{ {{-120x-120=-2880} \atop {120x+220y=3780}} \right.`

`100y=900\\y=9`

`x+y=24\\x+9=24\\x=15`