To solve the problem, we need to set up a system of equations.
We know that the family is buying a number of hamburger buns and a number of hot dog buns, so we need to assign a variable to each. I'll set x as the number of packages hamburger buns and y as the number of packages of hot dog buns.
We know that the total number of packages the family buys is 12, so one of the equations must be:
x + y = 12
To find out how many packages of buns the family buys, we need to set up an equation that equals the total contribution, twenty dollars.
If a package of hamburger buns costs two dollars and a package of hot dog buns costs one dollar and fifty cents, we could need to set up the equation as such:
2x + 1.5y = 20
To find out how many packages of hot dog buns the family bought, you would first solve for x in the second equation.
2x+1.5y=20
2x=20-1.5y
x=10-0.75y
Now you can take this and substitute it into the first equation for the x value, then solve for y.
10-0.75y+y=12
10+0.25y=12
0.25y=2
y= 8
This means the family bought 8 packages of hot dog buns, and if you want to substitute it back into the first equation to solve for the number of packages of hamburger buns, you will get that they bought four packages of hamburger buns.
When you plug the x and y values back into the second equation to check my work, you will see that they make the equation true.
