Answer:
The mixture B is a lighter shade of purple.
Step-by-step explanation:
In order to answer the question, we first need to calculate the proportion of purple in both mixtures. The mixture that has the lowest proportion of purple will be the lighter one.
For mixture A :
5 cups of purple
2 cups of white paint
⇒ Mixture A is made with 5 + 2 = 7 cups of paint in which 5 are cups of purple. Therefore, we can calculate the proportion of purple as :
[tex]\frac{5CupsOfPurple}{7CupsInTheMixture}=\frac{5}{7}=0.7143[/tex]
This means that approximately 71.43% of the mixture A is made of purple paint.
For mixture B :
15 cups of purple paint
8 cups of white paint
⇒ Mixture B is made with 15 + 8 = 23 cups of paint in which 15 are cups of purple. Therefore, we can calculate the proportion of purple as :
[tex]\frac{15CupsOfPurple}{23CupsInTheMixture}=\frac{15}{23}=0.6522[/tex]
This means that approximately 65.22% of the mixture B is made of purple paint.
If we compare the proportions :
[tex]0.7143>0.6522[/tex] ⇒ [tex]Proportion_{A}>Proportion_{B}[/tex]
We conclude that the mixture B is a lighter shade of purple because it has the lowest proportion of purple (we can also think that mixture B has the highest proportion of white)
