Answer:
Sam's test score is 46.5 and Nicole's score is 34.
Step-by-step explanation:
Let Sam's test score be [tex]s[/tex]
and
Nicole's score be [tex]n[/tex].
Then the relation is that,
[tex]s=n+12.5---eqn(1)[/tex]
The sum of twice Sam's score and three times Nicole's score is 195 gives the equation,
[tex]2s+3n=195---eqn(2)[/tex]
We put equation (1) into equation (2) to get,
[tex]2(n+12.5)+3n=195[/tex]
We expand to get,
[tex]2n+25+3n=195[/tex]
We group like terms to get,
[tex]2n+3n=195-25[/tex]
[tex]\Rightarrow 5n=170[/tex]
We divide both sides by 5 to get,
[tex]n=34[/tex]
We put the value of [tex]n[/tex] into equation (1) to get,
[tex]s=34+12.5[/tex]
[tex]s=46.5[/tex]
Therefore Sam's test score is 46.5 and Nicole's score is 34.
