Mixture. A mechanic has 363 gallons of gasoline and 17 gallons of oil to make gas/oil mixtures. He wants one mixture to be 6 % oil and the other mixture to be 2

Question

Mixture. A mechanic has 363 gallons of gasoline and 17 gallons of oil to make gas/oil mixtures. He wants one mixture to be 6 % oil and the other mixture to be 2.5 % oil. If he wants to use all of the gas and oil, how many gallons of gas and oil are in each of the resulting mixtures?

Round your answers to two decimal places

Answer 1

g₁ + g₂ = 363

o₁ + o₂ = 17

 

o₁ / g₁ = 0.06 ⇒ o₁ = 0.06g₁

o₂ / g₂ = 0.025 ⇒ o₂ = 0.025g₂

 

0.06g₁ + 0.025g₂  = 17

g₁ + g₂ = 363

 

Now solve the system for g₁ or g₂ using the method of your choice.

 

 

Answer 2

Bryson,

You need a system of equations to solve for the two quantities. Start by writing equations for the given information.

 

We know the total volume of the two mixtures must equal the starting volume of 363 + 17, so if we assign the quantity of 6% A, and we assign the quantity of 2.5% B, then we can write the equation:

 

A + B = 380 

 

We can also break down the gas and oil:

 

.06A + .025B = 17

 

.94A + .975B = 363

 

If we solve these two, whether by elimination, substitution, or by matrix, we get:

 

A = 214.29         B = 165.71

 

You can use the first equation to verify that they add up to the right volume.

If you need the breakdown of each, just plug them into the equations you solved.