solve the following mathematical problem:

In a survey at an airport, 55 travelers said that last year they had been to Spain, 53 to France and 79 to Germany, 18 had been to Spain and France, 17 to Spain and Germany and 25 to France and Germany, while 10 had to all three countries. How many travelers took part in the survey?

solve the following mathematical problem:

A family has 480kg of rice for X number of weeks. If they need to use the same amount for 4 more weeks, they need to cut down their weekly assumption of rice by 4kg. What is the value of X?

solve the following mathematical problem:

if $\cos \left(A+B\right)=\frac{1}{\sqrt{2}} and \cos \left(A-B\right)=\frac{\sqrt{3}}{2}, 0^{\circ }<\left(A+B\right)\le {90}^{\circ } and A>B, find the value of A and B.$

solve the following mathematical problem:

A shopkeeper sells two shirts at the same price. He makes 10% profit on one and loses 10% the other. How much in percentage does he gain or lose?

solve the following mathematical problem:

$if a=x{y}^{p-1}, b=x{y}^{q-1}, c=x{y}^{r-1} and p+q+r=3, then prove that a^{q-r}\times b^{r-p}\times c^{p-q}=1$

solve the following mathematical problem:

Price of 3 tables and 5 chairs is Tk. 2,000. Again, price of 5 tables and 7 chairs is Tk 3,200. What is the price of 1 table and 1 chair?