Question 1174670
let x = the 87% oil.
let y = the 93.5% oil.


x + y must be equal to 50.
that's your first equation.


.87 * x + .935 * y must be equal to .915 * 50
simplify this to get:
.87 * x + .935 * y = 45.75
that's your second equation.


these two equations need to be solved simultaneously.


start with:


x + y = 50
.87 * x + .935 * y = 45.75


multiply both sides of your first equation  by .87 and leave your second equation as is to get:


.87 * x + .87 * y = .87 * 50
.87 * x + .935 * y = 45.75


simplify the first equation and leave the second equation as is to get:


.87 * x + .87 * y = 43.5
.87 * x + .935 * y = 45.75


subtract the first equation from the first to get;


.065 * y = 2.25


you have just reduced 2 equations with 2 unknowns to 1 equation with 1 unknown.


solve for y to get:


y = 2.25 /.065 = 34.61538462.


since x + y = 50, then you get:


y = 34.61538462.
x = 50 minus y = 15.38461538.


those values of x and y should be your answers.
to confirm, replace x and y in the two original equations to get:


x + y = 50 becomes 34.61538462 + 15.38461538 which becomes 50 = 50 which is true.


.87 * x + .935 * y = 45.75 becomes .87 * 34.61538462 + .935 * 15.38461538 = 45.75 which becomes 45.75 = 45.75 which is true.


both equations are true with the values of x and y that were calculated by solving the simultaneous equations.


this confirms the solution is correct.


your solution is that 34.62 gallons of 87% engine oil plus 15.38 gallons of 93.5%% engine oil get you 50 gallons of 91.5% engine oil.