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

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!
RELATED QUESTIONS
A storage container hols 120 liters of fuel which is 3% oil and 97% gas. HOw many liters (answered by richwmiller)
A storage tank contains 150 liters of fuel which is 3% oil (and 97% gasoline). How many... (answered by ankor@dixie-net.com)
A 2.5 ml solution is composed of .93% geranium oil, .1% peppermint oil, and 98.97% almond (answered by xinxin)
A storage tank contains 120 Litera of fuel which is 3% oil (97%) gasoline. How many... (answered by josmiceli)
Two cars get an oil change at the same service center. Each customer is charged a fee X... (answered by checkley79)
a chain saw requires a mixture of 2-cycle engine oil and gasoline. according to the... (answered by josmiceli)
the engine in Paul's weed whacker uses an oil gas mixture. The owners manual recommends... (answered by josmiceli)
Fifteen litres of fuel containing oil is available for a certain two-cycle engine. This (answered by Alan3354)
Fifteen litres of fuel containing 3.2% oil is available for a certain two-cycle engine.... (answered by josgarithmetic,ikleyn)