SOLUTION: Mary (m) is 4 years older than Rico (r). Ten years ago Mary was 3 times as old as Rico was then. a) how old are they now? b) determine if answer is correct by checking that it sa

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Mary (m) is 4 years older than Rico (r). Ten years ago Mary was 3 times as old as Rico was then. a) how old are they now? b) determine if answer is correct by checking that it sa      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 309614: Mary (m) is 4 years older than Rico (r). Ten years ago Mary was 3 times as old as Rico was then. a) how old are they now? b) determine if answer is correct by checking that it satisfies the conditions of the problem
m + 4 = r
r(3) = m -10 ???
I don't know how to set the equation up or figure an age if I don't have any ages to begin with.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

You are interpreting the sentences incorrectly.

Mary (m) is 4 years older than Rico (r). 

Think this way.  

A.  Mary is older than Rico
B.  Therefore m is greater than r and r is smaller than m
C.  Therefore you must add 4 to the smaller (r) in order for it
    to equal the larger (m).

Do you see that you have this exactly backward with your
m + 4 = r
"?
You added to the larger m, making it even larger, and then put that
equal to the smaller.  Do you now see why that is incorrect?  

You should have 

SMALLER + 4 = LARGER or

      r + 4 = m

Then for the second part

Ten years ago Mary was 3 times as old as Rico was then

Think this way:

A.  Ten years ago Mary was m-10 
B.  Ten years ago Rico was r-10

Therefore 

C.  m-10 WAS 3 times r-10
D.  The equation is m-10 = 3(r-10)

Do you see that your equation "r(3) = m -10" is wrong because you
multiplied Rico's PRESENT age by 3 when you should have instead
multiplied his age TEN YEARS AGO by 3.

So the correct system of two equations in two unknowns m and r is

system%28++r+%2B+4+=+m%2C+m-10+=+3%28r-10%29%29

Do you know how to solve that system of eauations?  If not
post again asking how to solve that system.

Answer: m = 16, r = 12


 b) determine if answer is correct by checking that it satisfies the conditions of the problem 


Mary is 16, which makes her 4 years older than Rico, who is 12. Ten years ago
Mary was 16-10 or 6, and Rico was 12-10 or 2, and 6 is indeed 3 times 2, which
is how old Rico was then.

So it checks.

Edwin