SOLUTION: A certain car ideally requires an engine oil which is composed of 91.50% base oil and the rest in additives. How many gallons of 87.00% engine oil and how many gallons of 93.50% en

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Question 1174670: A certain car ideally requires an engine oil which is composed of 91.50% base oil and the rest in additives. How many gallons of 87.00% engine oil and how many gallons of 93.50% engine oil must be combined to produce 50.00 gallons of 91.50% engine oil? rounded up 2 decimals.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.

Answer by MathTherapy(10551) (Show Source):
You can put this solution on YOUR website!

A certain car ideally requires an engine oil which is composed of 91.50% base oil and the rest in additives. How many gallons of 87.00% engine oil and how many gallons of 93.50% engine oil must be combined to produce 50.00 gallons of 91.50% engine oil? rounded up 2 decimals.

Let amount of 87% oil be E
Then amount of 93.5% oil = 50 - E
We then get: .87E + .935(50 - E) = .915(50)
.87E + .935(50) - .935E = .915(50)
.87E - .935E = .915(50) - .935(50)
- .065E = - .02(50)
Amount of 87% oil, or
It should be easy for you to find the amount of 93.5% oil!