the weigth of the student on earth is 610 Newtons
![\begin{gathered} F=99\text{ Newtons} \\ G=6.67\cdot10^(-11)\frac{m^3}{\operatorname{kg}s^2} \\ M=7.35\cdot10^(22)\text{ kg} \\ m=61\text{ kg} \\ r=1.74\cdot10^6m \end{gathered}]()
the weigth on the moon is 99 Newtons
Step-by-step explanation
Step 1
find the weigth on earth
the weigth on earth is given
let

then, let
m= 61 kg
g= 10 m/s^2
replace,

therefore, the weigth of the student on earth is 610 Newtons
Step 2
Now, the expression to gravitacional force between two objects is given by:
![\begin{gathered} F=G(Mm)/(r^2) \\ \text{where} \\ G\text{ is the gravitational constant} \\ G=6.67\cdot10^(-11)\frac{m^3}{\operatorname{kg}s^2} \\ M\text{ is the larger mass} \\ m\text{ is the smaller mass} \\ r\text{ is the distance betw}en\text{ the center of the objects} \end{gathered}]()
then , to find the G on the moon
let
![\begin{gathered} M=7.35\cdot10^(22)\text{ kg},\text{ m=61 kg} \\ r=1.74\cdot10^6m \\ \text{replace} \\ F=G(Mm)/(r^2) \\ F=6.67\cdot10^(-11)\frac{m^3}{\operatorname{kg}s^2}\cdot\frac{7.35\cdot10^(22)\text{ kg}\cdot61\text{ kg}}{(1.74\cdot10^6m)^2} \\ F=6.67\cdot10^(-11)\frac{m^3}{\operatorname{kg}s^2}\frac{7.35\cdot10^(22)\text{ kg}\cdot61\text{ kg}}{(3.02\cdot10^(12)m^2^{}} \\ F=6.67\cdot10^(-11)\frac{m^3}{\operatorname{kg}s^2}\cdot1.48\cdot10^(12) \\ F=99\text{ Newtons} \end{gathered}]()
Step 3
finally, we have the force and the mass, so we can get the g value on the moon

I hope this helps you