A certain customer at a restaurant calculates his tip by adding a cons

Set the cost of the meal itself as x and the tip percentage as y. We know x*(1 + y) = 24.

Statement 1:

Now we have (x + 4)*y = 4.8. Then we have \(y = \frac{4.8}{x + 4}\). Plug in above to get:

\(x*(1 + \frac{4.8}{x + 4}) = 24\)

\(x*\frac{x + 8.8}{x + 4} = 24\)

\(x^2 + 8.8x = 24x + 96\)

\(x^2 - 15.2x - 96 = 0\)

Note we don't have to solve this. Since the constant is negative, there will be only one positive solution for x, so sufficient.

Statement 2:

Similar to above, we have \((x - 6)y = 3.8\) and \(y = \frac{3.8}{x - 6}\).

\(x*(1 + \frac{3.8}{x - 6}) = 24\)

\(x*\frac{x - 2.2}{x - 6} = 24\)

\(x^2 - 2.2x = 24x - 144\)

\(x^2 - 26.2x + 144 = 0\)

The constant is positive while the x term is negative, so there are two possible positive solutions. Insufficient.

Ans: A

Note: Statement B should be "a tip of 2.8" as from A we know x = 20 and y = 20%.
_________________

Let us assume the constant be c and x be tip percentage of total bill.
Now tip will be c + 24*x

Statement 1 - c + 28 * x = 4.8 Not sufficient
Statement 2 - c + 18 * x = 3.8 Not sufficient

When both statements are taken together, the eqn can be solved
C is correct answer