Scott and Greg were asked to add two whole numbers. Instead, Scott subtracted the two numbers and got 16, and Greg multiplied them and got 1305. What was the correct sum?

One number is 29, and the other one 45

Step-by-step explanation:

Solve this problem by creating two equations that represents the statements, and solve for the unknowns using substitution:

Let's say that one of the numbers is X , and the other one Y, and assume that Y is larger than X, so when we do their difference we get the 16 units they mention in the problem:

Y - X = 16

The info on the  product of the two numbers will give us our second equation:

X * Y = 1305

Now use the first equation to substitute Y with 16 + X, in the second equation:

X (16 + X) = 1305

16 X + X^2 = 1305

X^2 + 16 X - 1305 = 0

Now use the quadratic formula to solve for X, and we get two possible answers: X = -45 or X = 29

So, since we are looking for whole numbers, we discard the negative answer, and keep X = 29

Then, the value of the other number "Y" is = 29 + 16 = 45

If Lana's age is L, her youngest sister is L/2 (or 0.5L) and the twins L-2.  Add all these together (remember that there are two sisters who are L-2 years old):
0.5L + L-2 + L-2 + L = 45
Simplify the L's by adding them all together, we get:
3.5L - 2 - 2 = 45
3.5L - 4 = 45
Now add 4 to both sides:
3.5L = 49
Now divide both sides by 3.5
L = 49/3.5 = 14.  Now we know that Laura is 14, so her youngest sister must be 7.