- #1

harpazo

- 208

- 16

- Homework Statement
- Find Tanya's present age by setting up a system of equations and using the substitution method.

- Relevant Equations
- T = M + 28

T + 6 = 3(M + 6)

Tanya is 28 years older than Marcus. In 6 years, Tanya will be three times as old as Marcus. How old is Tanya now?

Let T = Tanya

Let M = Marcus

Set Up:

T = M + 28...Equation A

T + 6 = 3(M + 6)...Equation B

Solve Equation A for M.

T = M + 28

T - 28 = M

Substitute T - 28 into Equation B.

T + 28 = 3(T - 28 + 6)

T + 28 = 3(T - 22)

T + 28 = 3T - 66

T - 3T = -66 - 28

-2T = -94

T = -94/-2

T = 47

Tanya is 47 years old.

What about checking the answer? I need to find M first.

Let T = 47

T = M + 28

47 = M + 28

47 - 28 = M

19 = M

Marcus is 19 years old.

Is 47 > 19 by 28?

Well, 19 + 28 = 47.

I conclude that Tanya is 47 years old.

Let T = Tanya

Let M = Marcus

Set Up:

T = M + 28...Equation A

T + 6 = 3(M + 6)...Equation B

Solve Equation A for M.

T = M + 28

T - 28 = M

Substitute T - 28 into Equation B.

T + 28 = 3(T - 28 + 6)

T + 28 = 3(T - 22)

T + 28 = 3T - 66

T - 3T = -66 - 28

-2T = -94

T = -94/-2

T = 47

Tanya is 47 years old.

What about checking the answer? I need to find M first.

Let T = 47

T = M + 28

47 = M + 28

47 - 28 = M

19 = M

Marcus is 19 years old.

Is 47 > 19 by 28?

Well, 19 + 28 = 47.

I conclude that Tanya is 47 years old.