Linear Application Problem

Question

In two years Bob will be three times as old as Al. 8 years ago, Bob was 5 times his age. How old is Bob now?

Answer 1

Dear Angela,

     I am first going to set up the data in a small table:

 

Bob                                            Al

 

  X= Bob's age              Let Y= Al 's age    current ages             

 

 

(X+2) = 3 (Y+ 2)                                     two years later

 

(X-8)= 5 (Y-8)                                           Eight years ago

 

(X-8)= 5Y-40

                          Simplify, and use distributive property.

(X+2)=3Y+ 6      Multiply equation on right by -1.

 

 

X-8= 5Y -40

-x-2= -3Y-6

  -10= 2Y -46    Add +46 to both sides of equal sign.

-10+46 =2Y      36=2Y     Y=36/2=18            Then  substitute Y=18 into one of the original equations.

 

 

X-8 = 5Y - 40                               Solve for "X."

 

X= 5Y- 40 +8                        X=5(18)-32= 90-32= 58

 

 

Next, just check your work by substituting "X" and "Y"values into  (X-8)= 5Y-40 and (X+2)=3Y+ 6 . If the

 

equations are true, your answer is correct.

 

If you have any questions, let me know.  Also, if you like my work, please give me a thumbs up.

                                                                           Susan C.

 

             

 

 

 

 

Answer 2

let b = Bob and a = Al

Here's what we know:

b + 2 = 3(a + 2)

b - 8 = 8(a - 8)

 

Distribute:

b + 2 = 3a + 6
b - 8 = 8a - 64

 

Isolate b (-2 in first equation; +8 in the second):

b = 3a + 4
b = 8a - 56
 

Since both equal b, they also equal one another:

3a + 4 = 8a - 56

4 = 5a - 56

60 = 5a

12 = a

 

Now we can solve for b:

b = 3 * 12 + 4

b = 36 + 4

b = 40

 

Check:

b = 8 * 12 - 56

b = 96 - 56

b = 40