Question

Perfect Purple Water The recipe for Perfect Purple Water says, "Mix 8 ml of blue water with 3 ml of red water." lada mixes 24 ml of blue water with 9 ml of red water. Andre mixes 16 ml of blue water with 9 ml of red water. . Which person will get a color mixture that is the same shade as Perfect Purple Water? Explain or show your reasoning.​

Answer 1

Lada will get a color mixture that is the same shade as Perfect Purple Water.

Explanation:

Proportions

The mix for Perfect Purple Water contains 8 ml of blue water with 3 ml of red water.

The exact proportion of both ingredients is, blue to red:

`\displaystyle (8)/(3)`

Lada mixes 24 ml of blue water with 9 ml of red water. The proportion is:

`\displaystyle (24)/(9)`

Simplifying by 3:

`\displaystyle (8)/(3)`

The proportion obtained by Lada is the same shade as Perfect Purple Water.

Andre mixes 16 ml of blue water with 9 ml of red water, his proportion is:

`\displaystyle (16)/(9)`

This fraction cannot be reduced and its result is not exactly the same as the perfect required proportion.

Thus, Lada will get a color mixture that is the same shade as Perfect Purple Water.

Answer 2

Analysing the question:

We are given that the ratio between the blue and red color is 8 : 3

as long as the volumes of the colours added simplify to 8 : 3 , the color will be Perfect Purple

Lada's Solution:

Lada mixed 24 mL of blue water with 9 mL of red water

we will try to simplify this ratio:

24:9 = 24 / 9

8 / 3

8 : 3

Hence, the ratio of the colours in Lada's mixture is correct. So, Lada will get perfect purple water

Andre's Solution:

Andre mixed 16mL of Blue water with 9 mL of red water

we will try to simplify this ratio:

16 : 9 = 16 / 9

THIS RATIO CANNOT BE SIMPLIFIED

Hence, the ratio of blue and red color in Andre's mixture is 16 : 9

but the ratio for a perfect purple color is 8 : 3

Since the ratio in Andre's mixture is incorrect, she will NOT get the perfect purple colour