Any Math Whizzers Out There?

**Maximus** · 02-04-2012, 07:52 PM

An algebra question in one of my classes:
Mike's age is 3/4 of Mary's age. In five years, Mike's age will be 7/9 Mary's age. How old is Mike now?

I should be on my bike. Instead, I'm on my iPhone.

**mehush** · 02-04-2012, 09:29 PM

Simultaneous Linear Equations.

Mikes age being A

Marys age being B

A=3/4B , A+5=7/9B

Solve for B in the second equation by plugging in 3/4B for A

3/4B + 5= 7/9B, do the math, then plug the value you get for B back in to the first equation.....and viola.........I think.

It's been a while.

**reidmct** · 02-04-2012, 09:32 PM

Mike's age is 3/4 of Mary's age. In five years, Mike's age will be 7/9 Mary's age. How old is Mike now?

I haven't proofed my work so there very well could be a mistake, since these problems usually are deisgned to result in whole numbers or simple fractions.... Hey, you gotta work at least a little on this! At least I'm giving you the approach: It is a quadratic equation.

GIVEN:
M=Mike's age
R=Mary's age
M=3/4R
M+5=7/9(R+5)

The problem reduces to a quadratic equation.Here's the step-by-step to get there:
3/4R+5=7/9(R+5)
3/4R=7/9(R+5)-5
3/4R=7/9R+7/9*5-5
3/4R=7/9R+35/9-5
3/4R=7/9R+35/9-45/9
3/4R=7/9R-10/9
3/4R*9=(7/9R-10/9)*9
27/4R=7R-10
27/4R-7R=-10
27/4R-7R+10=0
4R*(27/4R-7R+10)=0*4R
27-28R^2+40R=0
-28R^2+40R+27=0 (A quadratic equation -- ax^2+bx+c = 0)

All quadratic equations are solved as x = (-b+- SQRT(b^2-4ac)/2a

In this case, x=R

b^2-4ac = 40^2-4*-28*27 = 1600-(-3024) = 1600+3024 = 4624

SQRT(4624)=68

-b = -40

2a = -28*2 = -56

So,
x = (-40+68)/-56 = -0.5
or
x = (-40-68)/-56 = 1.928571

So, Mary's age is 1.928571
Mike's age is 3/4(1.928571) = 1.446429

**XXXXL** · 02-04-2012, 09:34 PM

i read the problem to tammy (who is a chief financial officer)and who loves doing taxes for a hobby. she started talking about mike and mary having some argument or something that was totally over my head. some formulas,

then looked on algebra.com and the answer is there.

mike is 30 and mary is 40

**reidmct** · 02-04-2012, 09:34 PM

If Mehush's answer is "correct," then the person who wrote the problem made a mistake. Mehush's solution assumes that Mary does not age 5 years while Mike is aging 5 years.

**reidmct** · 02-04-2012, 09:48 PM

Originally Posted by XXXXL

i read the problem to tammy (who is a chief financial officer)and who loves doing taxes for a hobby. she started talking about mike and mary having some argument or something that was totally over my head. some formulas,

then looked on algebra.com and the answer is there.

mike is 30 and mary is 40

Aaacckkk!

Indeed, algebra.com is right, and I... am wrong.

All my beautiful work, down the drain. Why? Because I made a mistake.

I violated the frickin' Associative rule! Remember have the Distributive and Associative rules that Mrs. Bean hammered into your little Jr. High head? And being thankful you'd never need to know that crap again? Hah!

I am chagrined.

Nothing like showing off your quadratic chops, only to discover it was a simple solution... the kind you learn to do in like the second week of 6th Grade. So ashamed!

**DWC** · 02-04-2012, 10:43 PM

Originally Posted by XXXXL

i read the problem to tammy (who is a chief financial officer)and who loves doing taxes for a hobby. she started talking about mike and mary having some argument or something that was totally over my head. some formulas,

then looked on algebra.com and the answer is there.

mike is 30 and mary is 40

...... So ... Mikes hanging out with a Cougar? ......

**mehush** · 02-04-2012, 10:46 PM

Originally Posted by reidmct

If Mehush's answer is "correct," then the person who wrote the problem made a mistake. Mehush's solution assumes that Mary does not age 5 years while Mike is aging 5 years.

OOOPS

Guess I'm neither a wizard nor a whizzer.

**Maximus** · 02-04-2012, 11:15 PM

Originally Posted by DWC

Originally Posted by XXXXL

i read the problem to tammy (who is a chief financial officer)and who loves doing taxes for a hobby. she started talking about mike and mary having some argument or something that was totally over my head. some formulas,

then looked on algebra.com and the answer is there.

mike is 30 and mary is 40

...... So ... Mikes hanging out with a Cougar? ......

Exactly what I was thinkin'.

I should be on my bike. Instead, I'm on my iPhone.

**Maximus** · 02-04-2012, 11:21 PM

My daughter is a math guru and she can't figure it out. The 30 and 40 is right but she can't figure out how to get there. It's been too many years for me to do more than 1+1. I can't even figure out where you go on algebra.com to input the info.

I should be on my bike. Instead, I'm on my iPhone.