document.write( "Question 729873: Hi I am trying to do some word problems by using a system of equations, for example using x and y that way when I set up the two equations I can use either the subsitution method or elimination method. Here are my word problems hope you can help. (:\r
\n" ); document.write( "\n" ); document.write( "1. A total of $12,000 is invested, part at 6% simmple interest and part at 3%. If the annual return from the two investments is the same, how much is invested at each rate?\r
\n" ); document.write( "\n" ); document.write( "2. A car travels 225 kilometers in the same time that a truck travels 195 kilometers. If the speed of the car is 10 kilometers per hour faster than the speed of the truck, find the speed of each vehicle.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #446337 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
1. A total of $12,000 is invested, part at 6% simple interest and part at 3%.
\n" ); document.write( " If the annual return from the two investments is the same, how much is invested at each rate?
\n" ); document.write( "let x = amt invested at 6%
\n" ); document.write( "let y = amt invested at 3%
\n" ); document.write( "Two equations
\n" ); document.write( "x + y = 12000
\n" ); document.write( "and
\n" ); document.write( ".06x = .03y
\n" ); document.write( "divide both sides by .03, results
\n" ); document.write( "2x = y
\n" ); document.write( "replace y with 2x in the 1st equation
\n" ); document.write( "x + 2x = 12000
\n" ); document.write( "3x = 12000
\n" ); document.write( "x = 12000/3
\n" ); document.write( "x = 4000
\n" ); document.write( "I'll let you find y, check the solutions in the interest equation
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "2. A car travels 225 kilometers in the same time that a truck travels 195 kilometers.
\n" ); document.write( "let x = car speed, let y = truck speed
\n" ); document.write( "write a time equation; time = dist/speed
\n" ); document.write( "\"225%2Fx\" = \"195%2Fy\"
\n" ); document.write( "Cross multiply
\n" ); document.write( "225y = 195x
\n" ); document.write( "divide both sides by 5, results:
\n" ); document.write( "45y = 39x
\n" ); document.write( ":
\n" ); document.write( "\" If the speed of the car is 10 kilometers per hour faster than the speed of the truck,\"
\n" ); document.write( "x - y = 10
\n" ); document.write( "x = y + 10
\n" ); document.write( "\"find the speed of each vehicle.\"
\n" ); document.write( "replace x with (y+10) in the 1st simplified equation
\n" ); document.write( "45y = 39(y+10)
\n" ); document.write( "45y = 39y + 390
\n" ); document.write( "45y - 39y = 390
\n" ); document.write( "6y = 390
\n" ); document.write( "y = 390/6
\n" ); document.write( "y = 65 mph, the speed of the truck
\n" ); document.write( "I'll let you find the speed of the car, check your solutions in both equations\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "
\n" );