7. After tennis training, Andy collects twice as many balls as Roger and five more than Maria. They collect 35 balls in total. How many balls does Andy collect?
A 20
B 19
C 18
D 16
E 8
Solution: D
Suppose that Andy collects $x$ balls. Since Andy collects twice as many balls as Roger, Roger collects $\frac{1}{2} x$ balls. Andy collects five more balls than Maria. So Maria collects $x-5$ balls. So between them, Andy, Roger and Maria collect $x+\frac{1}{2} x+(x-5)$ balls. They collect 35 balls in total. Therefore
$$
x+\frac{1}{2} x+(x-5)=35 \text {. }
$$

Multiplying this equation by 2 gives
$$
2 x+x+2 x-10=70 .
$$

This is equivalent to
$$
5 x=80 \text {. }
$$

It follows that $x=16$.
Note: As we are asked for the number of balls that Andy collects, it is natural to begin the problem by letting $x$ be this number. However, we see then see that this leads to an equation which includes a fraction. If you look ahead, you might prefer to let the number of balls that Roger collects be $x$. Then Andy collects $2 x$ balls and Maria collects $2 x-5$ balls. We then obtain the equation
$$
2 x+x+(2 x-5)=35
$$
with no fractions in it. This equation is equivalent to $5 x=40$, from which we deduce that $x=8$. This calculation is easier that the one we gave above, but, if you use this method, you need to remember that the answer we are asked for is $2 x$ and not just $x$.