SOLUTION: A college student invested part of a $25,000 inheritance at 7% interest and the rest at 6%. If his annual interest is $1,671 how much did he invest at 6%? If I told you the answe

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A college student invested part of a $25,000 inheritance at 7% interest and the rest at 6%. If his annual interest is $1,671 how much did he invest at 6%? If I told you the answe      Log On


   

Question 308333: A college student invested part of a $25,000 inheritance at 7% interest and the rest at 6%. If his annual interest is $1,671 how much did he invest at 6%? If I told you the answer is $8,000, in your own words, using complete sentences, explain how you would solve the problem.
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say he invested x at 6%. Then he has 25000-x to invest at 7%.
The interest is
x%2A0.06%2B%2825000-x%29%2A0.07+=+1671
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=7900.00000000002.
  • Graphical form: Equation x%2A0.06%2B%2825000-x%29%2A0.07=1671 was fully solved.
  • Text form: x*0.06+(25000-x)*0.07=1671 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2A0.06%2B%2825000-x%29%2A0.07=1671+%29
    For tutors: simplify_cartoon( x*0.06+(25000-x)*0.07=1671 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%2A0.06%2B%28highlight_red%28+25000+%29-x%29%2A0.07=1671.
Moved 25000 to the right of expression
It becomes x%2A0.06%2B%28-x%2Bhighlight_green%28+25000+%29%29%2A0.07=1671.
Look at x%2A0.06%2B%28-x%2B25000%29%2A0.07=highlight_red%28+1671+%29.
Moved these terms to the left highlight_green%28+-1671+%29
It becomes x%2A0.06%2B%28-x%2B25000%29%2A0.07-highlight_green%28+1671+%29=0.
Look at x%2A0.06%2Bhighlight_red%28+%28-x%2B25000%29%2A0.07+%29-1671=0.
Expanded term 0.07 by using associative property on %28-x%2B25000%29
It becomes x%2A0.06-highlight_green%28+0.07%2Ax+%29%2Bhighlight_green%28+0.07%2A25000+%29-1671=0.
Look at x%2A0.06-0.07%2Ax%2Bhighlight_red%28+0.07%2A25000+%29-highlight_red%28+1671+%29=0.
Replace constants in expression: highlight_red%28+0.07%2A25000+%29,highlight_red%28+-1671+%29 with highlight_green%28+79.0000000000002+%29
It becomes highlight_green%28+79.0000000000002+%29%2Bx%2A0.06-0.07%2Ax=0.
Look at highlight_red%28+79.0000000000002+%29%2Bx%2A0.06-0.07%2Ax=0.
Moved 79.0000000000002 to the right of expression
It becomes x%2A0.06-0.07%2Ax%2Bhighlight_green%28+79.0000000000002+%29=0.
Look at highlight_red%28+x%2A0.06+%29-highlight_red%28+0.07%2Ax+%29%2B79.0000000000002=0.
Eliminated similar terms highlight_red%28+x%2A0.06+%29,highlight_red%28+-0.07%2Ax+%29 replacing them with highlight_green%28+%280.06-0.07%29%2Ax+%29
It becomes highlight_green%28+%280.06-0.07%29%2Ax+%29%2B79.0000000000002=0.
Look at %28highlight_red%28+0.06+%29-highlight_red%28+0.07+%29%29%2Ax%2B79.0000000000002=0.
Added fractions or integers together
It becomes %28-highlight_green%28+1%2F100+%29%29%2Ax%2B79.0000000000002=0.
Look at highlight_red%28+%28-highlight_red%28+1%2F100+%29%29%2Ax+%29%2B79.0000000000002=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F100+%29
It becomes -highlight_green%28+1+%29%2Fhighlight_green%28+100+%29%2Ax%2B79.0000000000002=0.
Look at highlight_red%28+-1%2F100%2Ax%2B79.0000000000002+%29=0.
Solved linear equation highlight_red%28+-1%2F100%2Ax%2B79.0000000000002=0+%29 equivalent to -0.01*x+79.0000000000002 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=7900.00000000002.

Universal Simplifier and Solver


Done!