Right now Seths age is 4/5 the age of his brother eric

Question

Twenty-one years ago, Eric was twice as old as Seth. What are their ages now?

Answer 1

Dear Donald,

     All of these calculations can also be placed in a table for easy viewing. 

 

                  Eric's Information                                          Seth's Information

    

 

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                                            Present Time                                                                 

Let X= Eric's age                                                            (4/5)X= Seth's age

 

Question:  What are their ages now?

 

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                                              Past (21 years ago)

X-21 =Eric's age                                                                (4/5)X-21=Seth's age

 

2*[4/5(X-21]=Eric's age

 

Therefore, X-21= 2*[4/5(X)-21]=Eric's age           Substitution

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X-21= 8/5 X  - 42         Solve for "X" by adding 42 to both sides.

 

X-21+42=(8/5) X

 

X+21 = (8/5)X              Subtract "X" from both sides.

 

21=(3/5)X                    Multiply both sides of equation by reciprocal of (3/5), which is 5/3

 

21*(5/3)= X                  Finish the problem to find value of "X," which is Eric's age.   

 

                                   Then find  4/5 (X)= Seth's age  

 

 

 

 

Answer 2

ANSWER: Seth is 28 and Eric is 35. The explanation follows:

 

1. Let's say Eric is x years old today

2. Seth is 4/5 the age of Eric which we just called x; therefore, Seth is (4/5)x years old today.

3. 21 years ago, Seth was (4/5)x-21 years old (just subtract 21 from his current age and Eric was x-21 years old.

4. We are told that 21 years ago, Eric was twice as old as Seth. So, Eric was 2{(4/5)x-21} years old 21 years ago (just multiply Seth's age 21 years ago by 2).

5. Now look back at step 4. When we multiply Seth's age 21 years ago by 2, we get Eric's age 21 years ago. We have have also said that Eric was x-21 years old 21 years ago (step #3). So we should set the two values equal to each other and solve for x.

2{(4/5)x-21}=x-21

When we solve this for x, we get x=35. So Eric is 35 years old today. Seth is (4/5) as old as Eric, therefore Seth is 

35(4/5) years old which  is 28.

 

If this helps, please vote up my answer. If not, please let me know how I may further assist you. 

Answer 3

21 years ago E = 2S

(S+21) = 4/5(E+21)

5S + 105 =8S + 84

21 = 3S

S = 7

E = 14

Ages now Seth is 28, Eric is 35