Allen is mixing red and yellow paint to make two different shades of orange. to make 1 cup of dark orange paint he needs 7 ounces of red paint and 1 ounce of yellow paint. to make 2 cups of light orange paint he needs 13 ounces of yellow paint and 3 ounces of red paint. allen decides to make 3 cups of dark orange paint and 3 cups of light orange paint. how many ounces of yellow paint does he need

42 ounces of yellow paint.

Step-by-step explanation:

To make three cups of dark orange, you just need to remember that to make one cup you need: 7 ounces of red paint and 1 ounce of yellow paint. Then, to make three cups, we just have to multiply these proportions by three,which means 7x3 ounces of red paint =21 ounces of red paint, plus 3x1 ounces of yellow paint =3 ounces of yellow paint. Then we need 21 ounces of red paint and 3 of yellow paint to make three cups of dark orange.To make one cup of light orange, we need 13 ounces of yellow paint, and 3 ounces of red paint. Then, to make three cups, we just multiply this proportion by 3, as follows: 13x3 ounces of yellow paint = 39; and 3x3 ounces of red paint =9.  Then we need 9 ounces of red paint and 39 of yellow paint to make three cups of light orange.Adding up the amount of ounces we need to make dark orange and light orange, we get a total amount of 21+9=30 ounces of red paint and 3+39=42 ounces of yellow paint to make three cups of light orange and three cups of dark orange.