Answer:
The prices must be $1.50 and $1.75
Step-by-step explanation:
For instance, seven hot dogs and two hamburgers cost $14: 7D+2B=14
We also know that two hot dogs and seven hamburgers cost $15.25: 2D+7B=15.25
Now, if we combine these two equations, we have a system where EVERYTHING has to be true at the same time
7D+2B=14
2D+7B=15.25
From here there are a couple trick you should know to solve a system of equation, especially substitution and elimination. I see a coefficient of 2, so I'd rather use substitution by dividing the entire first equation in half:
3.5D+B=7
Now I'll solve for B
B=7-3.5D
Now that I've solved for a variable, I can substitute the solution into the other equation
2D+7( B )=15.25
becomes
2D+7(7-3.5D)=15.25
Now I can distribute and solve for D:
2D+49-24.5D=15.25
22.5D=33.75
D=1.5
Now we can replace D from either (or both) of our original equations and see what B has to be
7(1.5)+2B=14
10.5+2B=14
2B=3.5
B=1.75
2(1.5)+7B=15.25
3+7B=15.25
7B=12.25
B=1.75
The prices must be $1.50 and $1.75. The most important part of all this is setting up the equations, the rest is just being careful with your calculations.
