Albert has a mixture of 4 drops of red food coloring in 7 pa

Albert has a mixture of 4 drops of red food coloring in 7 parts water. Betsy has 5 drops of red food coloring in 8 parts water. Carla says the mixtures will be the same color because Betsys mix has one more part of each in her mixture. If Carla is correct, explain why her reasoning is correct and use a ratio table to demonstrate the reasoning is correct in TWO different ways. If Carla is incorrect, explain why her reasoning is incorrect and use a ratio table to demonstrate in two different ways which solution is a darker red color.

Solution

Here we have that unit red food coloring in 1 part water in albert mixture = 4/7= 0 .5714

and unit red food coloring in 1 part of water in Betsy mixture = 5/8 = 0.625

So clearly 0.625 is greater density as compared to 0.5714

that means Carla`s reasoning is not correct as red part in both mixing are different , not same as she said here based on the unit ratio that means Betsy solution will be more darker red color as it is more dense for red color.

And one way to check it to convert both fractions in decimal form as we did in earlier steps,

and another ways is to make their denominators same first and then by comparing their numerators only.

So 4/7 = 4/7 x 8/8 = 32/56

and 5/8 = 5/8 x 7/7 = 35/ 54

so again Betsy fraction is more densed.