document.write( "Question 71908: You have asked your boss for a raise. He tells you that you are already the highest paid employee. You want to find out how much everyone else makes. the information you have is the following:
\n" ); document.write( "Monday - Al works 2 hours/ Cal works 4 hours/ Jim works 6 hours/ Tim works 5 hours/ You work 3 hours/ the total payroll for the day = $182.00\r
\n" ); document.write( "\n" ); document.write( "Tuesday - Al works 2 hours/ Cal works 0 hours/ Jim works 6 hours/ Tim works 0 hours/ You work 3 hours/ total payroll for the day = $87.00\r
\n" ); document.write( "\n" ); document.write( "Wednesday - Al works 2 hours/ Cal works 4 hours/ Jim works 0 hours/ Tim works 0 hours/ You work 3 hours/ total payroll = $79.00\r
\n" ); document.write( "\n" ); document.write( "Thursday - Al works 2 hours/ Cal works 0 hours/ Jim works 0 hours/ Tim works 5 hours/ You work 3 hours/ total payroll = $94.00\r
\n" ); document.write( "\n" ); document.write( "Friday - Al works 2 hours/ Cal works 4 hours/ Jim works 0 hours/ Tim works 5 hours/ You work 0 hours/ total payroll = $113.00
\n" ); document.write( "What is everyone's houly rate?
\n" ); document.write( "I tried to make this into equations for each day such as:
\n" ); document.write( "2a + 4c + 6j + 5t + 3y = 182 and 2a + 6j + 3y = 87
\n" ); document.write( "However I could not figure out how to solve these equations! I would be very grateful for some help, Thanks! \n" ); document.write( "

Algebra.Com's Answer #51400 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"2a+%2B+4c+%2B+6j+%2B+5t+%2B+3y+=+182\"$
\n" ); document.write( " $\"2a+%2B+0c+%2B+6j+%2B+0t+%2B+3y+=+87\"$
\n" ); document.write( " $\"2a+%2B+4c+%2B+0j+%2B+0t+%2B+3y+=+79\"$
\n" ); document.write( " $\"2a+%2B+0c+%2B+0j+%2B+5t+%2B+3y+=+94\"$
\n" ); document.write( " $\"2a+%2B+4c+%2B+0j+%2B+5t+%2B+0y+=+113\"$
\n" ); document.write( "First, I would subtract the 2nd from the 1st
\n" ); document.write( "That will give me c in terms of t
\n" ); document.write( " $\"+2a+%2B+4c+%2B+6j+%2B+5t+%2B+3y+=+182\"$
\n" ); document.write( " $\"-2a+-+0c+-+6j+-+0t+-+3y+=+-87\"$
\n" ); document.write( " $\"4c+%2B+5t+=+95\"$
\n" ); document.write( "Then, if I subtract the 4th from the 5th
\n" ); document.write( " $\"-2a+-+0c+-+0j+-+5t+-+3y+=+-94\"$
\n" ); document.write( " $\"+2a+%2B+4c+%2B+0j+%2B+5t+%2B+0y+=+113\"$
\n" ); document.write( " $\"4c+-+3y+=+19\"$
\n" ); document.write( "Now I subtract the 3rd from the 2nd
\n" ); document.write( " $\"+2a+%2B+0c+%2B+6j+%2B+0t+%2B+3y+=+87\"$
\n" ); document.write( " $\"-2a+-+4c+-+0j+-+0t+-+3y+=+-79\"$
\n" ); document.write( " $\"-4c+%2B+6j+=+8\"$
\n" ); document.write( "Now I'll add the 3rd to the 5th
\n" ); document.write( " $\"2a+%2B+4c+%2B+0j+%2B+0t+%2B+3y+=+79\"$
\n" ); document.write( " $\"2a+%2B+4c+%2B+0j+%2B+5t+%2B+0y+=+113\"$
\n" ); document.write( " $\"4a+%2B+8c+%2B+0j+%2B+5t+%2B+3y+=+192\"$
\n" ); document.write( "I'll subtract the 4th from this
\n" ); document.write( " $\"+4a+%2B+8c+%2B+0j+%2B+5t+%2B+3y+=+192\"$
\n" ); document.write( " $\"-2a+-+0c+-+0j+-+5t+-+3y+=+-94\"$
\n" ); document.write( " $\"2a+%2B+8c+=+98\"$
\n" ); document.write( "Putting my results together
\n" ); document.write( " $\"4c+%2B+5t+=+95\"$
\n" ); document.write( " $\"4c+-+3y+=+19\"$
\n" ); document.write( " $\"-4c+%2B+6j+=+8\"$
\n" ); document.write( " $\"8c+%2B+2a+=+98\"$
\n" ); document.write( "Now I'll rearrange them
\n" ); document.write( " $\"5t+=+95+-+4c\"$
\n" ); document.write( " $\"3y+=+4c+-+19\"$
\n" ); document.write( " $\"6j+=+4c+%2B+8\"$
\n" ); document.write( " $\"2a+=+98+-+8c\"$
\n" ); document.write( "Now plug these (5t,3y,6j,2a) into the 5th
\n" ); document.write( " $\"2a+%2B+4c+%2B+0j+%2B+5t+%2B+0y+=+113\"$
\n" ); document.write( " $\"98+-+8c+%2B+4c+%2B+95+-+4c++=+113\"$
\n" ); document.write( "combine terms
\n" ); document.write( " $\"+98+-+8c+%2B+95+=+113\"$
\n" ); document.write( " $\"-8c+=+113+-+193\"$
\n" ); document.write( " $\"8c+=+80\"$
\n" ); document.write( " $\"c+=+10\"$
\n" ); document.write( "from above
\n" ); document.write( " $\"5t+=+95+-+4%2A10\"$
\n" ); document.write( " $\"3y+=+4%2A10+-+19\"$
\n" ); document.write( " $\"6j+=+4%2A10+%2B+8\"$
\n" ); document.write( " $\"2a+=+98+-+8%2A10\"$
\n" ); document.write( "solving
\n" ); document.write( " $\"5t+=+95+-+40\"$
\n" ); document.write( " $\"t+=+11\"$
\n" ); document.write( " $\"3y+=+40+-+19\"$
\n" ); document.write( " $\"y+=+7\"$
\n" ); document.write( " $\"6j+=+40+%2B+8\"$
\n" ); document.write( " $\"j+=+8\"$
\n" ); document.write( " $\"2a+=+98+-+80\"$
\n" ); document.write( " $\"a+=+9\"$
\n" ); document.write( "So, I have
\n" ); document.write( " $\"a+=+9\"$
\n" ); document.write( " $\"c+=+10\"$
\n" ); document.write( " $\"j+=+8\"$
\n" ); document.write( " $\"t+=+11\"$
\n" ); document.write( " $\"y+=+7\"$
\n" ); document.write( "It looks like you're the lowest paid employee
\n" ); document.write( "check the results by plugging into all the original equations, like
\n" ); document.write( " $\"2a+%2B+4c+%2B+6j+%2B+5t+%2B+3y+=+182\"$
\n" ); document.write( " $\"2%2A9+%2B+4%2A10+%2B+6%2A8+%2B+5%2A11+%2B+3%2A7+=+182\"$
\n" ); document.write( " $\"18+%2B+40+%2B+48+%2B+55+%2B+21+=+182\"$
\n" ); document.write( " $\"182+=+182\"$
\n" ); document.write( "You can check the rest \n" ); document.write( "

\n" );