when grace and tony started their jobs their weekly salaries totaled $1300. Ten years later grace's salary has doubled and tonys salary has tripled. Together their weekly salaries now total $3200. How much did they each make 10 years ago?

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Step 1

Let's write down what we do know.

Grace's salary and Tony's salary equaled 1300

Let's arbitrarily call Grace's salary x, and Tony's salary y.

Then x +y=1300.

Next, we know that Grace's salary doubled, and Tony's salary tripled

Thus 2x+3y=?

Well the mystery is 3200, because that is what it listed

So

2x+3y=3200

Step 2: System of equations

2x+3y=3600

x+y=1300

(We need to have a common coeffient, so that when we subtract the two equations we are left with one variable. Let's multiply equation 2 by 2, and solve for y)

2x+3y=3600

2x+2y=2600 (Subtract the two equations)

0+y=1000

y=1000.

Thus Tony's salary was 1000. Now lets find Grace's by substituting it into the first equation

x+1000=1300

x=300

Thus Grace's salary was 300.

Therefore

Grace's salary was $300 dollars, and Tony's was $1000.

Notice if you wanted to check, substitute both salaries into the second equation

2(300)+3(1000) =3600

Which is the correct amount! .

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