Max creates a lavender dye by mixing 3 parts of red dye.
Will a mixture of 14 parts of blue dye with 23 parts of red dye create the same shade of lavender?
What does Max mix 3 parts of red dye with?
To determine if a mixture of 14 parts of blue dye with 23 parts of red dye will create the same shade of lavender as Max's mixture, we need to compare the ratios of red and blue dye in both mixtures.
Max's mixture has a ratio of 3 parts red dye to 0 parts blue dye (since only red dye is mentioned), which can be written as 3:0.
The mixture of 14 parts blue dye with 23 parts red dye has a ratio of 23 parts red dye to 14 parts blue dye, which can be written as 23:14.
To compare these ratios, we can simplify them by finding their greatest common divisor (GCD). In this case, the GCD of 3 and 0 is 3, and the GCD of 23 and 14 is 1.
To simplify the ratios, we divide both sides of each ratio by their respective GCD:
Max's mixture: 3 ÷ 3 : 0 ÷ 3 = 1:0
Mixture of 14 parts blue dye with 23 parts red dye: 23 ÷ 1 : 14 ÷ 1 = 23:14
As we can see, both mixtures have the ratio of 1:0 and 23:14 respectively. Since the ratios are different, the mixture of 14 parts of blue dye with 23 parts of red dye will not create the same shade of lavender as Max's mixture.