Question 246731
Ann's age is seven-tenths of bill's age.
Let Bill = x
Let Ann = 7/10 x
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If in 4 years ann's age will be eight-elevenths of bill's age, our equation becomes: 
{{{(7x/10)+4=(x+4)(8/11)}}}
Let's start finding common denominators to be able to add fractions.  Then we will worry about solving for x.
{{{(7x/10)+(40/10)=(x+4)(8/11)}}}
{{{(7x+40)/10=((x/1)(8/11))+((4/1)(8/11))}}}
{{{(7x+40)/10=(8x/11)+(32/11)}}}
{{{7x+40)/10=(8x+32)/11}}}
{{{(7x+40)/10)=((8x+32)/11)}}}
{{{(((7x+40)/10)(11/11))=(((8x+32)/11)(10/10))}}}
{{{(((11(7x+40))/110))=(((10(8x+32))/110))}}}
{{{(77x+440)/110=(80x+320)/110}}}
If we multiply by 110 on both sides of the equation, we get:
{{{77x+440=80x+320}}}
Now solve for x:
{{{440-320=80x-77x}}}
{{{120=3x}}}
{{{x=120/3}}}
{{{x=40}}} <-- Bill's age.
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Remember to check your answer by plugging this value in the original equation: {{{(7x/10)+4=(x+4)(8/11)}}} Both sides of the eqn must equal to each other.