Question 269775
Set Up:
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Let Mrs. Johson's age = A
Let the son's age = B

Equation 1: {{{A = 3B}}} (She is tree times as old as here son)
Equation 2: {{{A - 10 = 5*(B - 10)}}} (She was 5 times as old 10 years ago)

Solution:
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We can substitute 3B into equation 2 for A
Equation 2: {{{A - 10 = 5*(B - 10)}}}
{{{(3B) - 10 = 5*(B - 10)}}} Simplify
{{{3B - 10 = 5B - 50}}} Subtract 3B from both sides
{{{-10 = 5B - 50 - 3B}}} Add 50 to both sides
{{{50 - 10 = 5B - 3B}}} Simplify
{{{40 = 2B}}} Divide both sides by 2
{{{highlight(20 = b)}}}

Now we can plug 20 into equation 1 for B
Equation 1: {{{A = 3B}}}
{{{A = 3*(20)}}}
{{{highlight(A = 60)}}}

Check you Answers
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Plug you values back into both equations to check them
Equation 1: {{{A = 3B}}}
{{{60 = 3*(20)}}}
{{{highlight(60 = 60)}}}
Equation 2: {{{A - 10 = 5*(B - 10)}}}
{{{60 - 10 = 5*(20 - 10)}}}
{{{highlight(50 = 50)}}}