i am stuck on this question and don't know how to show my work. the question is,
John invests $1000 in mutual funds and bonds. If bonds earn 6% and mutual funds earn 8%, how much should he invest in each so that the interest from the mutual funds is double the interest from the bonds?
please help!!!
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I would start with "Let amount of money invested in bonds be $x$". Then, "Amount of money invested in bonds $=1000-x$".
Afterwards, I'll simply setup the relavant equations and solve for $x$.
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Let $B$ be the total in bonds Let $M$ be the total in mutual funds It follows that $M+B=1000\implies B=1000-M$. So we want to create another equation that deals with the interest. We basically want $.06M=2(.08(1000-M))$. So here is the equation. $$.06M=2(.08(1000-M))$$. So in essence all we needed was one equation. Solving this will get you the total money that should be invested in Mutual funds.
Construct your variables in this manner: Let x represent the amount of money invested into mutual funds. Let y represent the amount of money invested into bonds. What do you know about $x+y$? (hint: it is given in the question).
Next, construct your other linear equation: Use the second part of the information given to you. In particular, the interest earned by x and y can be represented as a coefficient in front of x and y. How should you arrange the equation to show that the amount of interest from x is double the amount of interest from y? (hint: what can do you to y in order to have an equality occur?)
Once these equations have been constructed, it is simple to solve for x and y!