For this problem, we can use systems of equations. I will use the variables <em>x </em> (for ice-cream) and <em>y</em> (for soda). We get the system:
2.25x+0.75y=30.00 x+y=18
Putting the second equation in terms of y, we get that y=-x+18. We can substitute this into our first equation.
2.25x+0.75y=30.00 becomes 2.25x+0.75(-x+18)=30
Solving for x, we get that x=11. This satisfies answer B.
However, if you want to check to see if this is correct, you could find y by plugging in your value of x into the first equation, then check to see if your found values satisfy BOTH equations.
2.25(11)+0.75y=30 24.75+0.75y=30 0.75y=5.25 y=7
Then we plug this into both equations to see if they are true.
2.25(11)+0.75(7)=30 24.75+5.25=30 30=30 (This is true)
x+y=18 11+7=18 18=18 (This is true).
Both equations are true, so the value for x and y are correct. We see that only answer B is supported through analyzing your work.
