A grocery clerk put only packages of flour tortillas and packages of corn tortillas on a shelf. The ratio of the number of flour tortillas to the number of packages on the shelf was 5 to 9. Which number could be the number of packages of corn tortillas the clerk put on the shelf?
Let's call the number of packages of flour tortillas "5x" (since the ratio of flour tortillas to total packages is 5 to 9, and we don't know the actual total). This means that the number of packages of corn tortillas is "9x" (since the total number of packages is 5x + 9x = 14x).
To figure out which number could be the number of packages of corn tortillas, we need to make sure that "9x" is a whole number. In other words, x must be a multiple of 1/9 (since we're scaling up by 9 to get the number of packages of corn tortillas).
Here are some possible values for x that would make "9x" a whole number:
- x = 1/9 (in this case, "9x" = 1, so the clerk put 1 package of corn tortillas on the shelf)
- x = 2/9 (in this case, "9x" = 2, so the clerk put 2 packages of corn tortillas on the shelf)
- x = 3/9 (in this case, "9x" = 3, so the clerk put 3 packages of corn tortillas on the shelf)
- x = 4/9 (in this case, "9x" = 4, so the clerk put 4 packages of corn tortillas on the shelf)
- and so on...
As you can see, any value of x that is a multiple of 1/9 will work. So, for example, the clerk could have put 5 packages of flour tortillas and 9 packages of corn tortillas on the shelf (in which case, x = 1/9 and "9x" = 1), or the clerk could have put 50 packages of flour tortillas and 90 packages of corn tortillas on the shelf (in which case, x = 10/9 and "9x" = 10).
No I think the answer is 9
If the clerk put 9 packages of corn tortillas on the shelf, then the total number of packages would be:
5 packages of flour tortillas + 9 packages of corn tortillas = 14 packages
And since the ratio of flour tortillas to total packages is 5 to 9, the number of packages of flour tortillas would be:
5/9 * 14 packages = 7.78 packages (rounded to two decimal places)
But since we can't have a fraction of a package, this means that 9 cannot be the correct answer.
As I explained before, any value of x that is a multiple of 1/9 could work. So for example, if the clerk put 45 packages of flour tortillas and 81 packages of corn tortillas on the shelf, then the ratio of flour tortillas to total packages would still be 5 to 9, and "9x" would equal 81, which is a whole number. Therefore, 81 could be the number of packages of corn tortillas the clerk put on the shelf.
f / (f+c) = 5/9
9 f = 5 f + 5 c
f = (5/4) c
looks to me like c can be any multiple of 4
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5 packages of flour tortillas + 9 packages of corn tortillas = 14 packages
WHOOPS
And since the ratio of flour tortillas to total packages is 5 to 9 (( NO ::: 5 to 14 )), the number of packages of flour tortillas would be:
You are correct, I apologize for my mistake. The correct ratio is 5 to 14, since the total number of packages is 5 + 9 = 14.
Using your equation f / (f+c) = 5/9, we can substitute f = (5/4) c to get:
(5/4) c / (c + (5/4) c) = 5/9
Simplifying the denominator:
(5/4) c / (9/4) c = 5/9
Cross-multiplying:
45 c = 20 c + 20 f
Substituting f = (5/4) c:
45 c = 20 c + 20 (5/4) c
45 c = 45 c
As you can see, c can indeed be any multiple of 4. So, for example, the clerk could have put 20 packages of flour tortillas and 36 packages of corn tortillas on the shelf (in which case, c = 36 and f = 45).
To find the possible number of packages of corn tortillas, we first need to understand the given ratio of flour tortillas to the total number of packages on the shelf.
Let's say the number of packages of flour tortillas is represented by "5x" (as there are 5 parts of flour tortillas in the ratio) and the total number of packages on the shelf is represented by "9x" (as there are 9 parts in the ratio).
The number of packages of corn tortillas can be found by subtracting the number of packages of flour tortillas from the total number of packages:
9x - 5x
This simplifies to:
4x
So, the number of packages of corn tortillas is represented by "4x".
To find the possibilities for the number of packages of corn tortillas, we need to determine the possible values of "x" that make "4x" a valid number.
Since "x" represents a positive integer, we can consider different values for "x" and see which ones give us a valid number.
For example, if we let "x" be 1, then the number of packages of corn tortillas would be:
4(1) = 4
If we let "x" be 2, then the number of packages of corn tortillas would be:
4(2) = 8
We need to continue this process until we find a value of "x" that gives us a possible number of packages of corn tortillas. So, there is no specific number that could be the number of packages of corn tortillas. It could be any multiple of 4.