Matrice word problem

[hollerback1]

Hi, I'm having trouble on this word problem.

The sum of the digits of a three-digit number is 18. Three times the tens digit minus 5 times the units digit is 17. If 4 times the units digit is added to twice the hundreds digit, the result is 22. Find the three-digit number.

please help me, Thanks.

 

[galactus]

Let the unit digit be a, the 100's digit be b, and the 10's digit be c.

a+b+c=18
-5a+3c=17
4a+2b=22

After you solve this system, enter you're results into \(\displaystyle 100b+10c+a\). That'll be your number. Check the problem's restraints and see if they work. I believe they will.

 

[pka]

The number is \(\displaystyle N = 100h + 10t + u\).
So \(\displaystyle \begin{array}{c}
{h + t + u = 18} \\
{3t - 5u = 17} \\
{4u + 2h = 22} \\
\end{array}\).

Now \(\displaystyle \left[ {\begin{array}{ccc}
1 & 1 & 1 \\
0 & 3 & { - 5} \\
2 & 0 & 4 \\
\end{array}} \right]\left[ {\begin{array}{c}
h \\
t \\
u \\
\end{array}} \right] = \left[ {\begin{array}{c}
{18} \\
{17} \\
{22} \\
\end{array}} \right]\)