Answer:
5 gallons of the 10% fructose solution.
15 gallons of 20% fructose solution
Step-by-step explanation:
You basically have an equation
Some amount of 10% solutions and some amount of 20% are to be combined to get to 17.5
So we can label those two amounts x and y, x being 10% and y being 20%.
We know that x + y (in gallons) must be equal to 20 gallons, so we can do this
x+y = 20
y = 20-x.
Then we can multiply x by 10% = 0.1x, 20-x by 20% which makes 4-0.2x
Then we know that the end result must be 20 gallons of 17.5% so we can multiply those two to get 3.5
Then we can add all of our results.
0.1x + 4 - 0.2x = 3.5
Solve for x
-0.1x = -0.5
x = 5
Now we have what x is, so we now know that there was 5 gallons of the 10% fructose solution.
Then we know that y = 20 - x so y is equal to 20 - 5 which is 15.
So that means that 15 gallons of 20% fructose solution was used.
So the answer is
5 gallons of the 10% fructose solution.
15 gallons of 20% fructose solution.
Hope this helped.
