a local hardware store has a 10-gallon can of gray paint left over that is a mixture of 35% black paint and 65% white paint. how many gallons of white paint will be needed to make the gray mixture 20% black?

Question

a local hardware store has a 10-gallon can of gray paint left over that is a mixture of 35% black paint and 65% white paint. how many gallons of white paint will be needed to make the gray mixture 20% black?

note: answers must be 5 gallons, 7.5 gallons, 12 gallons, or 17.5 gallons.

Answer 1

Well, it it contains .35*10 gallons of black paint now, then

black paint =.20*total
.35*10=.20(10+w)
right? solve for w

Answer 2

To solve this problem, we can set up an equation based on the information given.

Let's assume we need "x" gallons of white paint to make the gray mixture 20% black.

We know that the original gray mixture is 35% black paint and 65% white paint, which makes a total of 100%.

So, the total amount of black paint in the mixture is 10 gallons * 0.35 = 3.5 gallons.

Now, we need to find the new gray mixture which is 20% black. This means that 80% of the mixture will be white paint, while 20% will be black paint.

Since the total amount of the mixture remains the same (10 gallons), we can set up the equation:

x gallons (white paint) + 20/100 * 10 gallons (black paint) = 80/100 * 10 gallons (white paint)

Simplifying the equation:

x + 2 gallons (black paint) = 8 gallons (white paint)

Subtracting 2 gallons (black paint) from both sides:

x = 6 gallons (white paint)

So, to make the gray mixture 20% black, you will need 6 gallons of white paint.

However, the available answer options provided are 5 gallons, 7.5 gallons, 12 gallons, and 17.5 gallons. Since none of these options matches the calculated result of 6 gallons, it appears there might be an error or inconsistency in the question or answer choices.