Question

Pls help and give an explanation :)

You mix 4/5 quart of blue paint for every 1/3 quart of red paint to make 3 2/5 quarts of purple paint. How much blue paint and how much red paint do you use?

Answer 1

You would use one quart of red paint and 2.4 quarts of blue paint.

Explanation:

You first want to make 3 2/5 into a decimal. To do that you multiply 3x5 and add 2 which equals 17/5. Then you divide 17 by 5 and you get 3.4. So, now you know that you want your blue paint plus your red paint to equal 3.4 So, add 4/5 and 1/3 which equals 1.13333333333. Multiply 1.13333333333 and 3 which equals 3.4. So use the equation (4/5+1/3)x3 and you'll get 3.4. This shows that everything that you do was right.Then multiply just 1/3 x 3 and you'll get your answer which is 1. Then multiply just 4/5 x 3 and you'll get 2.4.

Answer 2

Let x be the amount of red paint used in quarts. Then, 4/5 of the blue paint used is 4/5 * x / (1/3) = 4 * 3 / 5 * x = 12/5 * x quarts.
The total amount of paint used is x + 12/5 * x = 17/5 * x quarts.
Since the total amount of paint used is 3 2/5 quarts, we have 17/5 * x = 3 2/5, which gives us x = 2/5 quarts of red paint.
So, the amount of blue paint used is 12/5 * 2/5 = 2 2/5 quarts.

Therefore, you use 2/5 quarts of red paint and 2 2/5 quarts of blue paint