A 50-gallon tank is filled with a 40% ethanol solution. How much solution should be drained but and replaced with an 80% ethanol solution to increase it to a 45% solution

How do you create your equations when working on a mixture word problem?

Let's try to think about the general form of a word problem involving mixtures.

In general, we have the following scenario:

a merchant sells two kinds of products (coffee, sweets, etc).

we know the unit prices for both kinds of products and for the final mixture

p

1

US dollars per pound for the first kind of product,

p

2

US dollars per pound for the second kind of product

p

m

US dollars per pound for the mixture

we know the total quantity formed by the mixture of the two products (

q

pounds)

we have to find out the quantities of each product needed to form the mixture

(here we have the variables:

x

denoting the quantity of the first kind of product and

y

denoting the quantity of the second kind of product)

Now, we have sufficient information to work out the equations.

First, we know that the sum of the two quantities is

q

pounds, which gives us the first equation:

x

+

y

=

q

Second, we know that the sale price is the product of quantity and unit price, which gives us the second equation:

p

1

x

+

p

2

y

=

p

m

⋅

q

Now, we have a system of two linear equations that can be easily solved by substitution.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)