Does it ever happen in your household: your kid comes home rather late after school and some after-school activities, as an exception you allow her to eat her dinner while doing this last page of homework, and a minute later the homework is soaking in milk. You pat the page with a paper towel, you dry it with a hair dryer - there is a hope, but some printed details are missing. Investigator or a looser - however you would like to call it, you have to help your child solve this impossible equation having too many unknowns:

208 ? X = 15 ? X

Question marks are placed here in the empty washed-out spots that used to have some arithmetic signs. What are these signs and what is X? (this puzzle is adapted from a Brain Busters book by B.R.Clarke)

Enter your answer on our Family Puzzle Marathon page. Solve three and get a prize!

## 9 comments:

208 - X = 15 + X

X = 96.5

Xo-xo-xo

Alin is back, sensing that Kim is catching up very fast.

I wonder if there are may be any additional answers....

Another answer:

208 - 13 = 15 * 13 = 195

OK, here's another rendition:

208 + (-96.5) = 15 - (-96.5)

X=-96.5 :-)

OK, here's another.

208 > 5 = 15 > 5

TRUE = TRUE

Think I am getting desperate to catch up with Alin?

OK, one more... (this one is less desperate looking!)

208/x = 15*x

208=15x^2

x^2=208/15

x=sqrt(208/15)

=approximately 3.7238

208 / 3.7238 = 15 * 3.7238

This is getting fun. Here's another approach:

208/x = 15-x

x(15-x)=208

15x-x^2=208 or x^2-15x+208=0

thus:

x = (15 +/- sqrt(225-4*208))/2

x = 7.5 +/- sqrt(-607)/2

x = 7.5 +/- i*sqrt(607)/2

We could do the same thing with

208/x = 15+x

the possibilities are endless!

Wow! How are we going to divide the winner's cake here? I already gave one piece to Alin. W gets another one. And Kim, I think she deserves at least three, topped with an ice cream and whipped cream!

I'm not sure I'd have given me credit for the logic version or the -96.5 one, but I'm happy to take whatever you're handing out. By the way, I thought of you all as I sipped mocha out of my Math Mom mug this morning. Enjoy the snow!

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