# SOLUTION: # 9. Mike invested \$7000 for one year. He invested part of it at 8% and the rest at 12%. At the end of the year he earned \$764 in interest. How much did he invest at each rate?

Algebra ->  Algebra  -> Expressions-with-variables -> SOLUTION: # 9. Mike invested \$7000 for one year. He invested part of it at 8% and the rest at 12%. At the end of the year he earned \$764 in interest. How much did he invest at each rate?       Log On

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 Click here to see ALL problems on Expressions-with-variables Question 190617: # 9. Mike invested \$7000 for one year. He invested part of it at 8% and the rest at 12%. At the end of the year he earned \$764 in interest. How much did he invest at each rate? Answer by jim_thompson5910(28593)   (Show Source): You can put this solution on YOUR website!# 9 Q: Mike invested \$7000 for one year. He invested part of it at 8% and the rest at 12%. At the end of the year he earned \$764 in interest. How much did he invest at each rate? A: Let x = amount of money Mike invests at 8% y = amount of money Mike invests at 12% Since "Mike invested \$7000 for one year.", this means that Also, because "He invested part of it at 8% and the rest at 12%. At the end of the year he earned \$764 in interest.", this translates to . Multiplying every term by 100 gets us So we have the system of equations: Let's solve this system by substitution Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the first equation Start with the first equation Subtract from both sides Rearrange the equation --------------------- Since , we can now replace each in the second equation with to solve for Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute to Multiply Combine like terms on the left side Subtract 84000 from both sides Combine like terms on the right side Divide both sides by -4 to isolate x Divide So this means that Mike invested \$1,900 at 8% ----------------------------- Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Combine like terms So Mike invested \$5,100 at 12% =============================================== Answer: So Mike invested \$1,900 at 8% and \$5,100 at 12%