Question 238495
Let A = Gloria's age
Let B = Theotis' age

Equation 1: {{{A = 4B}}} Because Gloria is 4 times older than Thesotis
Equation 2: {{{A - 3 = 7*(B - 3)}}} We are subtracting 3 from both sides because it was 3 years ago

In equation 1, we see that A = 4B, therefore we can substitute 4B into Equation 2 for A.
Equation 2: {{{A - 3 = 7*(B - 3)}}}
{{{4B - 3 = 7*(B - 3)}}} Simplify
{{{4B - 3 = 7B - 21}}} Add 21 to both sides
{{{21 + 4B - 3 = 7B}}} Subtract 4B from both sides
{{{21 - 3 = 7B - 4B}}} Combine like terms
{{{18 = 3B}}} Divide both sides by 3
{{{highlight(6 = B)}}}

So Theotis is 6.
To find Gloria' sage plug 6 into equation 1 for A
Equation 1: {{{A = 4B}}}
{{{A = 4*(6)}}}
{{{highlight(A = 24)}}}
Gloria is 24

You can check your answers by using A=24 & B=6 in equation 2
Equation 2: {{{A - 3 = 7*(B - 3)}}}
{{{24 - 3 = 7*(6 - 3)}}}
{{{21 = 7*(3)}}}
{{{21 = 21}}}