word problem help

Question

In 4 years Beth will be 3/4 Cate's age. 4 years ago Beth was 1/2 Cate's age.  How old are they now?

Answer 1

Let b = Beth's age now

Let c = Cate's age now

 

In 4 years Beth will be 3/4 Cate's age:

b+4 = (3/4)(c+4)

4b + 16 = 3(c+4)

4b+16 = 3c+12

4b - 3c = -4      {equation 1}

 

4 years ago Beth was half Cate's age:

b-4 = (1/2)(c-4)

2b - 8 = c - 4

2b - c = 4     {equation 2}

 

we now have two equations with 2 unknowns:

 

4b - 3c = -4    {equation 1}

2b - c = 4       {equation 2}

 

We Can solve by elimination or substitution.

To use elimination let's multiply 2nd equation

by -2 and add to eliminate b and solve for c.

 

4b - 3c = -4

-4b +2c = -8

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      -c = -12

       c = 12

Cate is 12 years old.

Plug this into equation 1 or 2 to solve for b.