1) A solid sphere of diameter “x” cm is melted to make 54 solid congruent hemispheres of diameter
0.06 m, without using calculator and showing all
necessary steps find exact value of x.

2) Surface area of 100 congruent solid spheres of
diameter “y” m is same as total surface area of 300
congruent solid hemispheres of diameter 10cm ,
find the exact value of y.

Mason and christian go to the movie theater and purchase refreshments for their friends. mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks. christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks. write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. using these equations, determine and state the price of a drink, to the nearest cent.