Homework Help: math

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

Math - Triangle ABC is inscribed in a circle such that A and B are the endpoints...
Geometry- how to write proof - ABC is a right triangle. Angle C is 90 degree. ...
Algebra 1 - Can anyone help me with these questions? Please 1. ac - bc + ad - bd...
maths - In a parallelogram ABCD, diagonals AC & BD intersect at O. E, F, G...
maths --plse help me.. - In a parallelogram ABCD, diagonals AC & BD ...
maths --plse help me.. - In a parallelogram ABCD, diagonals AC & BD ...
geometry - Given: ÚA≅ÚBDE; AB x DE = AD x BD...
Math - I do not understand this at all. Can someone please show all the steps sp...
geometry - if AB=CD, AB is 12-y, CD = 3x-4y, BD = 18, AC = x+y, what is x, y, ...
geometry - In Triangle ABC, AD is median. If AB is 8, BC is 18, AD is 7, find AC

For Further Reading

First Name:
School Subject:
Answer: