SOLUTION: woman's age is 7/10 of man's age. In 4 years the woman's age will be 8/11 of the man's age. How old is the man?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: woman's age is 7/10 of man's age. In 4 years the woman's age will be 8/11 of the man's age. How old is the man?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 105987: woman's age is 7/10 of man's age. In 4 years the woman's age will be 8/11 of the man's age. How old is the man?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
w=woman's age
m=man's age
.
A) w=7m/10
B) w+4=8(m+4)/11
.
A) 10w=7m
10w-7m=0
B) 11(w+4)=8(m+4)
11w+44=8m+32
11w-8m=32-44
11w-8m=-12
.
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

10%2Ax-7%2Ay=0
11%2Ax-8%2Ay=-12

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

-7%2Ay=0-10%2AxSubtract 10%2Ax from both sides

y=%280-10%2Ax%29%2F-7 Divide both sides by -7.


Which breaks down and reduces to



y=0%2B%2810%2F7%29%2Ax Now we've fully isolated y

Since y equals 0%2B%2810%2F7%29%2Ax we can substitute the expression 0%2B%2810%2F7%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


11%2Ax%2B-8%2Ahighlight%28%280%2B%2810%2F7%29%2Ax%29%29=-12 Replace y with 0%2B%2810%2F7%29%2Ax. Since this eliminates y, we can now solve for x.

11%2Ax-8%2A%280%29-8%2810%2F7%29x=-12 Distribute -8 to 0%2B%2810%2F7%29%2Ax

11%2Ax%2B0-%2880%2F7%29%2Ax=-12 Multiply



11%2Ax%2B0-%2880%2F7%29%2Ax=-12 Reduce any fractions

11%2Ax-%2880%2F7%29%2Ax=-12%2B0Add 0 to both sides


11%2Ax-%2880%2F7%29%2Ax=-12 Combine the terms on the right side



%2877%2F7%29%2Ax-%2880%2F7%29x=-12 Make 11 into a fraction with a denominator of 7

%28-3%2F7%29%2Ax=-12 Now combine the terms on the left side.


cross%28%287%2F-3%29%28-3%2F7%29%29x=%28-12%2F1%29%287%2F-3%29 Multiply both sides by 7%2F-3. This will cancel out -3%2F7 and isolate x

So when we multiply -12%2F1 and 7%2F-3 (and simplify) we get



x=28 <---------------------------------One answer

Now that we know that x=28, lets substitute that in for x to solve for y

11%2828%29-8%2Ay=-12 Plug in x=28 into the 2nd equation

308-8%2Ay=-12 Multiply

-8%2Ay=-12-308Subtract 308 from both sides

-8%2Ay=-320 Combine the terms on the right side

cross%28%281%2F-8%29%28-8%29%29%2Ay=%28-320%2F1%29%281%2F-8%29 Multiply both sides by 1%2F-8. This will cancel out -8 on the left side.

y=-320%2F-8 Multiply the terms on the right side


y=40 Reduce


So this is the other answer


y=40<---------------------------------Other answer


So our solution is

x=28 and y=40

which can also look like

(28,40)

Notice if we graph the equations (if you need help with graphing, check out this solver)

10%2Ax-7%2Ay=0
11%2Ax-8%2Ay=-12

we get


graph of 10%2Ax-7%2Ay=0 (red) and 11%2Ax-8%2Ay=-12 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.


and we can see that the two equations intersect at (28,40). This verifies our answer.


-----------------------------------------------------------------------------------------------
Check:

Plug in (28,40) into the system of equations


Let x=28 and y=40. Now plug those values into the equation 10%2Ax-7%2Ay=0

10%2A%2828%29-7%2A%2840%29=0 Plug in x=28 and y=40


280-280=0 Multiply


0=0 Add


0=0 Reduce. Since this equation is true the solution works.


So the solution (28,40) satisfies 10%2Ax-7%2Ay=0



Let x=28 and y=40. Now plug those values into the equation 11%2Ax-8%2Ay=-12

11%2A%2828%29-8%2A%2840%29=-12 Plug in x=28 and y=40


308-320=-12 Multiply


-12=-12 Add


-12=-12 Reduce. Since this equation is true the solution works.


So the solution (28,40) satisfies 11%2Ax-8%2Ay=-12


Since the solution (28,40) satisfies the system of equations


10%2Ax-7%2Ay=0
11%2Ax-8%2Ay=-12


this verifies our answer.



Check:
w=28, m=40
28=7*40/10...28=280/10 true
28+4=8*44/11...32=8*4 true
Ed