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PROBLEM SOLVING

[tex]__________________________[/tex]

Two years ago, I was three times as old as my brother was. In three years, I will be twice as old as my brother. How old are we now?

Step 1: Translate the statements into an equation.

We can represent my age as x and my brother's age as y.

The first statement can be translated as x - 2 = 3(y - 2) where;

• x - 2 is my age two years ago
• 3(y - 2) is my brother's age two years ago

The second statement can be translated as x + 3 = 2(y + 3) where;

• x + 3 is my age three years from now
• 2(y + 3) is my brother's age three years from now

Step 2: Write the equation into standard form or ax + by = c by transposing the terms.

First equation:

[tex]\sf x - 2 = 3(y - 2)[/tex]

[tex]\sf x - 2 = 3y -6[/tex]

[tex]\sf x - 2 + 2= 3y -6 + 2[/tex]

[tex]\sf x = 3y - 4[/tex]

[tex]\sf x - 3y= 3y - 3y - 4[/tex]

[tex] \boxed{ \sf x - 3y= - 4}[/tex]

Second equation:

[tex]\sf x + 3 = 2(y + 3)[/tex]

[tex]\sf x + 3 = 2y + 6[/tex]

[tex]\sf x + 3 - 3= 2y + 6 - 3[/tex]

[tex]\sf x = 2y + 3[/tex]

[tex]\sf x - 2y= 2y - 2y + 3[/tex]

[tex] \boxed{ \sf x - 2y= 3}[/tex]

Step 3: Solve for the value of x and y.

[tex]\sf \large \left \{ {{x \: - \: 3y \: = \: - 4} \atop {x \: - \: 2y \: = \: 3}} \right.[/tex]

Refer to the attachment for the solution for this part.

The value that we got for x is 17 and for y is 7.

∴ My age is 17 years old and my brother's age is 7 years old.