The balance of friendship

YES

Let $\displaystyle A_{1}$ be the area of the larger piston and $\displaystyle A_{2}$ be the area of the smaller one, which gives us $\displaystyle A_{1}=1.4A_{2}$ .

Let $\displaystyle F_{1}$ be the force applied on the larger piston. Then $\displaystyle F_{1}$ is the weight of Mike plus the weight of the chair, which means $\displaystyle F_{1}=1000+W$ .

Let $\displaystyle F_{2}$ be the force applied on the smaller piston. Then $\displaystyle F_{2}$ is the weight of Chris, which means $\displaystyle F_{2}=750 N$ .

Then we have $\displaystyle \dfrac{F_{1}}{A_{1}}=\dfrac{F_{2}}{A_{2}} \rightarrow \dfrac{1000+W}{1.4A_{2}}=\dfrac{750}{A_{2}}$

Manipulating the equation we find $\displaystyle W=1.4 \times 750 -1000 \rightarrow W=50 N$

Now making $\displaystyle W=mg$ and assuming $\displaystyle g=9.8 \dfrac{m}{s^{2}}$ we find $\displaystyle 50=9.8m \rightarrow m \approx 5.1 kg$

The closest integer is $\boxed{5}$ which is our answer.