Answer:
The number of packages of flour tortillas is a 9 multiple.
Step-by-step explanation:
Given there are only packages of flour tortillas and packages of corn tortillas on the shelf.
Let the number of flour tortillas be x and the number of corn tortillas be y
therefore the total number of packages are x+y.
Given the ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 7 to 16.
which means [tex]\frac{y}{x+y} = \frac{7}{16}[/tex]
[tex]16y = 7x+7y[/tex]
[tex]7x=9y[/tex]
[tex]x=\frac{9y}{7}[/tex]
since both x and y are integers y is in the form of 7k where k∈N.
[tex]x=9k[/tex]
Therefore x is a 9 multiple.
The number of packages of flour tortillas the clerk put on the shelf is multiple of 9.
Let there are x number of corn tortilla packages
Let there are y number of flour tortilla packages.
Total number of packages on the shelf = x + y
Then, by given data, we have:
[tex]\dfrac{7}{16} = \dfrac{x}{x+y}\\\\7x + 7y = 16x\\\\7y = 9x\\\\y = \dfrac{9}{7}x\\[/tex]
Since y is the count of number of flour tortilla packages, thus its integer and as 9 and 7 are relative primes, thus we have x as multiple of 7 and y as multiple of 9.
Thus, number of packages of flour tortillas the clerk put on the shelf is multiple of 9.
Learn more about ratio related problems here:
https://brainly.com/question/1504221
