in 10 years, harriet will be 3 times as old as she was 10 years ago. how old is she now?

Question

Looking for a solution to solve this problem that does not use algebra. (I,e, table or chart)

Answer 1

Hi Seleah,

 

Since we can't use Algebra let's try a successive approximation numerical technique.  We will guess a starting point let's arbitrarily use 15 years old for Harriet's age.  We can't use anything less than 11 years because the problem inclues her age from 10 years earlier, and in 10 years she will be 25 years old. That is 5 times as old as she was 10 years earlier.  

 

(15+10)/(15-10) = 25/5 = 5

 

Since we are trying to find a number where she is 3 times as old, the age needs to increase.  Let us try 3 years older so 18 years old.

 

(18+10)/(18-10) = 28/8 = 3.5

 

We are still a bit too high so let us try 4 years more, 22 years old.

 

(22+10)/(22-10) = 32/12 = 2 2/3

 

We have overshot 3 so let's go back halfway or -2 to 20 years old.

 

(20+10)/(20-10) = 30/10 = 3

 

Therefore 20 years old is Harriet's age

 

I hope this helps

 

 

Answer 2

Look for a pattern

 

Age 10 years ago          Age now                 Age in 10 years -    Is this 3 times as old as 10 years ago?

1                                   11                           21                        no - it is 21 times

2                                   12                           22                        no - it is 11 times

3                                   13                           23                        no its

4                                   14                           24                        no it is 6 times

5                                   15                           25                        no it is 5

6                                   16                           26                        no it is between 4 and 5 times

7                                   17                           27                        no it is a little less than 4 time

8                                   18                           28

9                                   19                           29                          

10                                 20                           30                   yes - age in 10 is three times more than 10 years ago

11                                 21                           31

x                                  x + 10                      3x

 

 

 

Do you see how the factor decreases as the age increases? Every year after age 1 has a lower multiple for the age that is 20 years older