A grocery clerk put only packages of flour tortillas and packages of corn tortillas on a shelf. The ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 5 to 9. Which number could be the number of packages of flour tortillas the clerk put on the shelf
Let's call the number of packages of corn tortillas "5x" (since the ratio is 5 to 9, and we can think of it as "5 out of 9 parts"). And let's call the total number of packages on the shelf "9x" (since the ratio is 9 in total).
From this, we can see that the number of packages of flour tortillas is simply "9x - 5x," which simplifies to "4x."
So any number that is a multiple of 4 could be the number of packages of flour tortillas on the shelf. For example:
- If there were 20 packages of corn tortillas on the shelf (5x), then there would be 36 total packages on the shelf (9x) and 16 packages of flour tortillas (4x).
- If there were 30 packages of corn tortillas on the shelf (5x), then there would be 54 total packages on the shelf (9x) and 24 packages of flour tortillas (4x).
- If there were 40 packages of corn tortillas on the shelf (5x), then there would be 72 total packages on the shelf (9x) and 32 packages of flour tortillas (4x).
And so on.
A grocery clerk put only packages of flour tortillas and packages of corn tortillas on a shelf. The ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 5 to 9. Which number could be the number of packages of flour tortillas the clerk put on the shelf?
A. 18
B. 14
C. 32
D. 23
The correct answer is C.
As explained in the previous answer, we know that the number of packages of flour tortillas is 4 times the number of packages of corn tortillas (since the ratio of corn tortillas to the total is 5:9, which means that flour tortillas must be 4 out of 9 parts).
Therefore, we need to find a multiple of 4 that, when added to a multiple of 5, gives us a multiple of 9.
Out of the options given, only 32 satisfies this condition:
- 5/9 * 32 = 17.78 (not a whole number)
- 4/9 * 32 = 14.22 (not a whole number)
This means that there are 20 packages of corn tortillas (5/9 of the total) and 32 packages of flour tortillas (4/9 of the total) on the shelf.
Let's assume the number of packages of corn tortillas is represented by "5x" and the total number of packages on the shelf is represented by "9x".
To find the number of packages of flour tortillas, we need to subtract the number of packages of corn tortillas from the total number of packages.
Number of packages of flour tortillas = Total number of packages - Number of packages of corn tortillas
Number of packages of flour tortillas = 9x - 5x
Number of packages of flour tortillas = 4x
Since x can represent any positive whole number, the number of packages of flour tortillas could be any multiple of 4.
To solve this problem, we can set up a proportion using the given information.
Let's represent the number of packages of corn tortillas as "5x" and the total number of packages on the shelf as "9x" (since the ratio of corn tortillas to the total number of packages is 5 to 9).
So, the number of packages of flour tortillas would be "9x - 5x" (since the total number of packages minus the number of packages of corn tortillas would give us the number of packages of flour tortillas).
To find the possible number of packages of flour tortillas, we need to determine a value for "x" that would result in a non-negative number of packages of flour tortillas. Since we can't have a negative number of packages, we need to solve the inequality:
9x - 5x ≥ 0
Simplifying this inequality, we get:
4x ≥ 0
Dividing both sides of the inequality by 4, we have:
x ≥ 0
Since x represents the number of packages of corn tortillas, it must be a non-negative value (greater than or equal to zero). Therefore, any positive value of x could be the number of packages of flour tortillas the clerk put on the shelf.
In conclusion, any positive number could be the number of packages of flour tortillas the clerk put on the shelf, as long as the ratio of corn tortillas to the total number of packages is maintained.