How much of a solution that is 18% fertilizer must be mixed with a solution that is 30% fertilizer to get 50 gallons of solution that is 27% fertilizer?

Question

I would just like to know the answer it’s ok if you don’t explain it

Answer 1

The total amount of the two types being mixed must add to 50 gallons.

So if we use x gallons of 18% fertilizer

We then add to that (50-x) gallons of 30% fertilizer

 

Look at the concentrations of actual fertilizer.

We have 0.18x gallons of actual fertilizer, added to 0.3(50-x) gallons of

actual fertilizer.. summing to 50 gallons of 27% fertilizer which is 0.27(50)

 

Your equation is:

0.18x + 0.3(50-x) = 0.27(50)

Multiply through by 100 to clear the decimals

18x + 30(50-x) = 27(50)

18x + 1500 - 30x = 1350

-12x + 1500 = 1350

 

If you finish solving for x from this point that is the number of gallons

of 18% fertilizer solution.

Then use 50-x to find the number of gallons of 30% fertilizer solution.