Answer
We bought $3$ one-pound bags of peanuts and $2$ three-pound bags of peanuts.
Work Step by Step
We need to set up a system of equations to find the solution.
First, we need to define two variables:
$x$ = the number of one-pound bags of peanuts purchased
$y$ = the number of three-pound bags of peanuts purchased
$5$ bags of peanuts will be bought so $x + y = 5$.
One-pound bags of peanuts are $2$ dollars each whereas the three-pound bags are $5.50$ dollars apiece. The total cost is $17$ dollars so $2x + 5.5y = 17$
Let us put the two equations together to solve for $x$ and $y$:
$x + y = 5$
$2x + 5.5y = 17$
Let us multiply the first equation by $2$ so that the $x$ terms for both equations can cancel each other out, leaving only the $y$ terms:
$2x + 2y = 10$
$2x + 5.5y = 17$
We subtract the second equation from the first equation:
$(2x+2y)-(2x+5.5y)=10-17\\
2x+2y-2x-5.5y=-7\\
-3.5y=-7$
y = \frac{-7}{-3.5}\\
y=2$
We can now use the value for $y$ to substitute into the first equation ($x + y = 5$) to find the value for $x$:
$x+y=5\\
x + 2 = 5\\
x=5-2\\
x=3$
We now know that we bought $3$ one-pound bags of peanuts and $2$ three-pound bags of peanuts.
