Posted by **sh** on Thursday, February 19, 2009 at 8:17pm.

ab+cd=34

ac+bd=38

ad+bc=43

what is a+b+c+d=?

multiple choice:

a)15 b)16 c)17 d)18 e)19

First, I tried guessing and testing, but couldn't find the correct answer.

Then I tried isolating a

a=(34-cd)/b

I'm stuck, there are too many variables

- math -
**drwls**, Thursday, February 19, 2009 at 9:07pm
In general, you are correct. There are not enough equations to solve for four variable. However they may be looking only for answers a,b,c,d that are integers. That restricts your options. Note that:

ab + cd + ac + bd = (a+d)(b+c) = 72

ab + ad + cd + bc = (a+c)(b+d) = 77

ac + bd + ad + bc = (a+b)(c+d) = 81

IF the solutions must be single-digit integers, the last equation tells you that

a + b = 9 and

c + d = 9

Therefore

a + b + c + d = 18

To solve for all four, you could say that

a + c = 11

b + d = 7

Which is consistent with a+b+c+d = 18

I can't find a way of satisfying

(a+d)(b+c) = 72

such that the sum of the two factors is 18.

I give up.

- math -
**sh**, Friday, February 20, 2009 at 1:11am
Wow, I never thought of combining it, thanks! The problem doesn't ask to solve for a b c & d

## Answer This Question

## Related Questions

- Statistical concept 68-95-99.7 - 1. A student taking a midterm exam in Ancient ...
- Stat HW for. - 1. A student taking a midterm exam in Ancient History comes to ...
- math - Beth Dahlke is taking a ten question multiple choice test for which each ...
- math - Beth Dahlke is taking a ten question multiple choice test for which each ...
- Calculus - Using l'hopitals rule, evaluate the following: Lim x-->infinity ...
- Math - a 10 question multiple choice test has 4 possible answer for each ...
- math - What is the probability of guessing 70 out of 100 multiple choice ...
- math - I have 4 spinners each divided into 4 equal sections (labeled 1,2,3,4,) ...
- Math - (x+4)(x-9)=0 I need help because I have tried all the answers as this a ...
- Stats - An instructor gives a test with 20 multiple choice questions. There are ...

More Related Questions