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?
A) 23
B) 18
C) 14
D) 32
5 + 9 = ?
14 🤦♀️🤦♀️🤦♀️🤦♀️
To figure out the possible number of packages of corn tortillas the clerk put on the shelf, we need to determine the ratio of flour tortillas to corn tortilla packages.
The ratio given states that the number of flour tortillas to the total number of packages is 5 to 9. So, for every 5 parts of flour tortillas, there are 9 parts of total packages, which includes corn tortillas.
To find the possible number of packages of corn tortillas, we can set up a proportion:
5/9 = Number of flour tortillas / Number of corn tortilla packages
Let's now check each option to see if it satisfies the proportion:
A) 23 packages of corn tortillas:
5/9 = Number of flour tortillas / 23
Cross-multiplying, we get: 5 * 23 = 9 * Number of flour tortillas
115 = 9 * Number of flour tortillas
The number of flour tortillas would not be a whole number in this case, so option A is not possible.
B) 18 packages of corn tortillas:
5/9 = Number of flour tortillas / 18
Cross-multiplying, we get: 5 * 18 = 9 * Number of flour tortillas
90 = 9 * Number of flour tortillas
Dividing both sides by 9, we get: Number of flour tortillas = 10
The number of flour tortillas is a whole number in this case, so option B is possible.
C) 14 packages of corn tortillas:
5/9 = Number of flour tortillas / 14
Cross-multiplying, we get: 5 * 14 = 9 * Number of flour tortillas
70 = 9 * Number of flour tortillas
The number of flour tortillas would not be a whole number in this case, so option C is not possible.
D) 32 packages of corn tortillas:
5/9 = Number of flour tortillas / 32
Cross-multiplying, we get: 5 * 32 = 9 * Number of flour tortillas
160 = 9 * Number of flour tortillas
The number of flour tortillas would not be a whole number in this case, so option D is not possible.
In conclusion, the only possible number of packages of corn tortillas the clerk could have put on the shelf is 18, which corresponds to option B.