Answer:
Part a) [tex]6\frac{2}{3}\ cups\ of\ purple\ paint[/tex]
Part b) [tex]4\ cups\ of\ blue\ paint[/tex] and [tex]2\ cups\ of\ red\ paint[/tex]
Step-by-step explanation:
The correct question is
Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 of a cup of white paint. Elena has 2/3 of a cup of white paint.
a) Assuming she has enough red paint and blue paint, how much purple paint can Elena make?
b) How much blue paint and red paint will Elena need to use with the 2/3 of a cup of white paint?
Part a)
we know that
Elena makes her favorite shade of purple paint by mixing
3 cups of blue paint
1 1/2 cups of red paint (1 1/2=1.5)
1/2 cup of white paint (1/2=0.5)
so
the ratio is 3:1.5:0.5
That means -----> For every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)
using proportion
Find out how much purple paint can Elena make with 2/3 of a cup of white paint
Let
x -----> the number of cups of purple paint
[tex]\frac{5}{0.5}=\frac{x}{(2/3)}\\\\x=(2/3)*5/0.5\\\\x=\frac{20}{3}\ cups\ of\ purple\ paint[/tex]
Convert to mixed number
[tex]\frac{20}{3}=\frac{18}{3}+\frac{2}{3}=6\frac{2}{3}\ cups\ of\ purple\ paint[/tex]
Part b)
Find out how much blue paint can Elena make with 2/3 of a cup of white paint
Let
x -----> the number of cups of blue paint
[tex]\frac{3}{0.5}=\frac{x}{(2/3)}\\\\x=(2/3)*3/0.5\\\\x=4\ cups\ of\ blue\ paint[/tex]
Find out how much red paint can Elena make with 2/3 of a cup of white paint
Let
x -----> the number of cups of red paint
[tex]\frac{1.5}{0.5}=\frac{x}{(2/3)}\\\\x=(2/3)*1.5/0.5\\\\x=2\ cups\ of\ red\ paint[/tex]
