Answer:
4 tours.
Explanation:
Let x represent number of tours.
We have been given that 4 tour groups took a trip to the national museum. There are 35 people in each group.
Let us find total number of people in 4 groups.
![\text{Total number of people in 4 groups}=35* 4](https://img.qammunity.org/2021/formulas/mathematics/high-school/tyhyw4zr1ailo879lrjxrsj23nlvzfo5lh.png)
![\text{Total number of people in 4 groups}=140](https://img.qammunity.org/2021/formulas/mathematics/high-school/mox517l2fiwdstcwb3vny14jo02lumb2d1.png)
We are also told that a maximum of 40 people were allowed on a tour at 1 time. So people who will see museum in x tours would be
.
The number of people who will visit museum in x tours should be greater than or equal to 140.
![40x\geq 140](https://img.qammunity.org/2021/formulas/mathematics/high-school/vy4zla9jcqw4nc497h7wx06bh2yot7wzi4.png)
![(40x)/(40)\geq (140)/(40)](https://img.qammunity.org/2021/formulas/mathematics/high-school/kntoi1j96628oxi9boimpzh5d6aj4ltjp1.png)
![x\geq 3.5](https://img.qammunity.org/2021/formulas/mathematics/high-school/bycce2bo6v2lbj3qk10jpsvhvibz8rebzs.png)
Since we cannot take 0.5 of a tour, therefore, the least number of tours that needed for all the people to take the tour would be 4.