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

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) (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



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
  

RELATED QUESTIONS

Mary (m) is 4 years older than Rico (r).  Ten years ago Mary was 3 times as old as Rico... (answered by ankor@dixie-net.com)
Jack is 24 years older than Mary is now. Four years ago, he was seven times as old as... (answered by josmiceli)
John is 3 years older than Mary. Five years ago he was four times as old as Mary was... (answered by josgarithmetic,MathTherapy)
Mary is 18 years older than Gabe. 15 years ago, Mary was 4 times as old as Gabe. How old... (answered by math_helper,stanbon)
rico is 3 times as old his son. four years ago he was 4 times as old as his son was at... (answered by TimothyLamb)
Miriam is four years older than ricardo. Ten years ago Miriam was 3 times as old as... (answered by stanbon)
John is ten years older than Mary. Five years ago, John was double Mary's age. How old... (answered by Maths68)
Rowena's age is three more than twice Mary's age. three years ago, Rowena was four times... (answered by ankor@dixie-net.com)
ten years from now tom will be twice as old as jane was when mary was nine times old as... (answered by ankor@dixie-net.com)