Formulate but do not solve the problem.

A private investment club has $$350,000$ earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high$-$risk, medium$-$risk, and low$-$risk. Management estimates that high$-$risk stocks will have a return rate of $16\%$; medium$-$risk stocks, $11\%$; and low$-$risk stocks, $4\%.$ The members have decided that the investment in low$-$risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $$35,000$ on the total investment. $($Assume that all the money available for investment is invested. Let $x,y,$ and $z$ denote the amount, in dollars, invested in high$-,$ medium$-,$ and low$-$risk stocks, respectively.$)$

$$

$=350,000$

$=z$

$=35,000$

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