In this problem, we will find the volume of the ellipsoid given by 1 25 49 16 we will do this by making a change of variables to convert the ellipsoid to the unit sphere in the new variables (u, v, w). a change of variables that will do this is:
x = 7 u.
y = 4 v
z = 5 w.
volume = 140
hint: the volume of the unit ball x2 y2 + z2 = 1 is 3

The students at jefferson middle school are raising money for a charity by selling t-shirts and hats. the number of t-shirts sold was 3 times the number of hats. the profit was $5 for each t-shirt sold and $2.50 for each hat sold. the students raised $840 for the charity. they used the system below to analyze their success and found the solution to be (144, 48). 5x+2.50y=840 x=3y how much did they earn from t-shirt sales?