An Older Person Is 4 Years Older than five times the age of a younger person.The Sum of their ages is 22.Find their ages.

Question

Trying To Find Out The Sum Of Their Ages Having Trouble Finding And Figuring It Out I Need Help To Get This Question Answered.

Answer 1

Let's call X the age of the older person and Y the age of the younger person. We have 2 unknowns, therefore, we need 2 equations to solve for them:

 

1. The first equation is that the age of the older person, X, is 4 more than 5 times the age of the younger person, or:

                           

                  X=4+5Y

 

2. The second equation is that the sum of the older persons age, X, and the younger persons age, Y, is 22, or:

 

                 X+Y=22

 

3. Substituting the first equation for X into the second equation we get:

 

                (4+5Y)+Y=22        substituting 4+5Y for X

                4+6Y=22               simplify

                4+6Y-4=22-4         subtracting 4 from both sides

                6Y=18                   simplify

                (6Y)/6=18/6          divide both sides by 6

                Y=3                      age of younger person

 

4. Now that Y is found, substitute 3 for Y in either equation to solve for X:

 

               X+Y=22         original equation

               X+3=22         substitute 3 for Y

               X+3-3=22-3   subtract 3 from both sides

               X=19             age of older person

 

5. After the answers are found check them in both equations:

 

               X=4+5Y         original equation                              X+Y=22             original equation

               19=4+5(3)     substituting 19 and 3 for X and Y      3+19=22           substituting for X and Y

               19=4+15       simplify                                           22=22               check

               19=19           check

 

Both equations check, therefore the math is correct and the answers are X=19 and Y=3.

Answer 2

Hi Michael.

 

Let's let

x = age of older person

y = age of younger person

 

The first sentence tells us

 

x = 5y+4

or

x-5y = 4

 

The second sentence tells us

x+y = 22

 

So we have our system of linear equations

 

x-5y=4

x+y=22

 

Using the elimination method, we need to eliminate one of the variables.  To do this we need one set of variables, either x or y, with coefficients that are equal in magnitude, but opposite in sign.

 

The x's both have a coefficient of 1 but they have the same sign.  If we multiply the second equation by -1, the coefficient of that x will be -1.

 

This gives us

x -5y = 4

-x-y=-22

 

Now add the two equations together, term by term.

 

-6y = -18

 

And solving for y, y=3

 

Now use y=3 in one of the original equations and solve for x.

 

x+y=22

x+3=22

x=19

 

So the older person is 19 and the younger person is 3.