One more problem. how to solve steps?

Question

Thank You everyone for all the help.

Could someone walk me through how to solve this question. I know there will be many coming up on a test I have.

Miss bass wants a 79% solution of herbicide to be mixed with a solution of 62% herbicide to form 34 litersof 66% solution. How many liters of the 79% solution must she use?

Thank You so much

Answer 1

Let X be the amount of 79% herbicide:
Let (34 - X) be the amount of 66% herbicide:

In words:
79% of X plus 62% of (34-X) should equal 66% of 34 liters:

In equation form:
79X + 62(34 - X) = 66(34)

I think you can take it from here...

Answer 2

This is long.. but I hope it helps!

You need to set up a system of equations, which is just a group of equations you can use to get the final answer.

We know there will be 34 liters total in the end, so we know that the amount of each solution added together is equal to 34:

x + y = 34

Then, for each liter of solution for x, there is 79% herbicide, the way to write this is 79/100 or .79. The 62% solution is 62/100 or .62. The final 66% solution is 66/100, or .66.

So we need x of the .79, and y of the .62 to make .66 for the 34 liters.

(x * .79) + (y * .62) = 34 * .66

.79x + .62y = 22.44

We have two variables now, x and y, so we'll solve the equation to get just the y variable:

.62y = 22.44 - .79x

y = (22.44 - .79x) / .62

Remember that x + y = 34 ? if we solve that for y now, we get:
y = 34 - x

So, since y always equals y (y=y), and we have two different equations that tell us what y is equal to, we can say that one equation is equal to the other one -- getting rid of the y so that we can solve them for X:

34 - x = (22.44 - .79x) / .62

.62 * (34 - x) = 22.44 - .79x

21.08 - .62x = 22.44 - .79x

.17x = 1.36

x = 8

Now, which one was x? oh yeah, the 79% solution. So 8 liters of the 79% solution...

34 - 8 = y, ==> 26 = y

so 26 liters of the 62% solution!


Remember, this is all based on the fact that x=x and y=y and so on... The trick is to get the two different formulas for y, then put one of the equations equal to the other equation, which takes the y variable out completely and only leaves the X!

Usually, one of the formulas is very simple, just the Total minus the X variable: T - x = y

Its often the second formula that takes the time to figure out!