Answer
To generate enough interest to cover the costs, $117,500$ dollars must be invested in a bond.
Work Step by Step
We assign the variables:
$x$ = country club memberships per month (725 dollars)
$12x$ = yearly country club membership
$y$ = allotment charged annually (700 dollars)
$z$ = amount invested in bond
Step 1:
Find the equation that represents the problem.
We can get the equation from the wording in the problem.
From "The dues for a country club membership are $\$725$ per month plus a $\$700$ allotment charged annually" and "a bond at $8\%$ to generate enough interest to cover the cost", we get
amount invested in the bond * 8% = yearly country club membership + allotment charged annually
So,
$0.08z=12x+y$
Step 2:
Solve for z
$0.08z=12(725)+700$
$0.08z=8700+700$
$0.08z=9400$
$z=\frac{9400}{0.08}$
$z=117500$
Step 3:
To generate enough interest to cover the costs, $117,500$ dollars must be invested in a bond.
