Please show solution. Ty. Answer the following problem. Show your complete solution.1. The amount of paint p needed to paint the walls of a room varies directly as the area A of thewall. If 2 gallons of paint is needed to paint a 40 sq meter wall, how many gallons of paintare needed to paint a wall with an area of 100 sq meters?

Given- The amount of paint p varies as the area Aof the wall and 2 gallons of paint is needed to paint a 40 m2 wall. To Find- The amount of paint needed to paint a wall with an area of 100 m2. Explanation- As per the question, it is given that the amount of paint p varies as the area Aof the wall, so mathematically we can write as follows, p∝Ap=K·Ap=KA .......1 Where K is an proportionality constant. As per the question, it is given that 2 gallons of paint is needed to paint a 40 m2 wall, so from the equation (1), it gives, 2=K·40K=240K=0.05 So, the equation (1) becomes, p=0.05A As we have to find the amount of paint needed to paint a wall with an area of 100 m2, from the above equation, p=0.05Ap=0.05·100p=5 gallons So, The amount of paint needed to paint a wall with an area of 100 m2 is 5 gallons. Answer- 5 gallons