Answer:
12 burgers, 0 sub sandwiches or 7 burgers, 5 sandwiches
Explanation
First, we need to form the equation. This will be 2.50x + 3.50y ≤ 30.
2.5x + 3.5y ≤ 30
Now I'll solve for x here, but you don't have to.
First I'll move 3.5y to the other side by subtracting that value from both sides.
2.5x ≤ -3.5y + 30
Next, divide by 2.5 to get just x on the left.
x ≤ -1.4y + 12
Now to substitute.
2.5(-1.4y + 12) + 3.5y ≤ 30
-3.5y + 30 + 3.5y ≤ 30
Wait a second...This creates... (canceling out -3.5y and 3.5y...)
30 ≤ 30
The two sides are the same! That means one solution has y being 0. 30/2.5 (as we already figured out) is 12. So one solution is (12, 0).
Solution 2 can be figured out with this. What is the LCM of 3.5 and 2.5? Here we really need to use 35 and 25.
First, to factorize.
25: 5 * 5
35: 5 * 7
A five in is common. So to get the LCM, we need to multiply 5 * 7 * 5 to get 175. However, since this is in TENTHS, it's actually 17.5 being the LCM between 3.5 and 2.5.
Since 7 * 2.5 = 17.5, as does 3.5 * 5, our other solution is (7, 5).