SOLUTION: ann's age is seven-tenths of bill's age.In 4 years ann's age will be eight-elevenths of bill's age.How old is bill now? 28,33,40,or 68

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Question 246731: ann's age is seven-tenths of bill's age.In 4 years ann's age will be eight-elevenths of bill's age.How old is bill now?
28,33,40,or 68
Found 2 solutions by College Student, stanbon:
Answer by College Student(505) About Me  (Show Source):
You can put this solution on YOUR website!
Ann's age is seven-tenths of bill's age.
Let Bill = x
Let Ann = 7/10 x
.
If in 4 years ann's age will be eight-elevenths of bill's age, our equation becomes:
%287x%2F10%29%2B4=%28x%2B4%29%288%2F11%29
Let's start finding common denominators to be able to add fractions. Then we will worry about solving for x.
%287x%2F10%29%2B%2840%2F10%29=%28x%2B4%29%288%2F11%29
%287x%2B40%29%2F10=%28%28x%2F1%29%288%2F11%29%29%2B%28%284%2F1%29%288%2F11%29%29
%287x%2B40%29%2F10=%288x%2F11%29%2B%2832%2F11%29
7x%2B40%29%2F10=%288x%2B32%29%2F11
%287x%2B40%29%2F10%29=%28%288x%2B32%29%2F11%29
%28%28%287x%2B40%29%2F10%29%2811%2F11%29%29=%28%28%288x%2B32%29%2F11%29%2810%2F10%29%29
%28%28%2811%287x%2B40%29%29%2F110%29%29=%28%28%2810%288x%2B32%29%29%2F110%29%29
%2877x%2B440%29%2F110=%2880x%2B320%29%2F110
If we multiply by 110 on both sides of the equation, we get:
77x%2B440=80x%2B320
Now solve for x:
440-320=80x-77x
120=3x
x=120%2F3
x=40 <-- Bill's age.
.
Remember to check your answer by plugging this value in the original equation: %287x%2F10%29%2B4=%28x%2B4%29%288%2F11%29 Both sides of the eqn must equal to each other.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
ann's age is seven-tenths of bill's age.In 4 years ann's age will be eight-elevenths of bill's age.How old is bill now?
28,33,40,or 68
------------
Let ann be "a".
Let bill = "b".
------
a = (7/10)b
(a+4) = (8/11)(b+4)
-----------
Substitute for "a" and solve for "b":
(78/10)b + 4 = (8/11)(b+4)
Multiply thru by 110 to get:
11*7b + 440 = 8*10(b+4)
77b + 440 = 80b + 320
3b = 120
b = 40 (Bill's age)
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Cheers,
Stan H.