Final answer:
To have an equal number of hamburgers and rolls, one must find the least common multiple (LCM) of the package sizes, which is 70. Thus, 7 packages of hamburger patties and 5 packages of rolls should be purchased.
Step-by-step explanation:
To determine the least number of hamburgers and rolls needed where the number of each is the same, we must find the least common multiple (LCM) of the package sizes.
Hamburger patties come in packages of 10 and rolls in packages of 14.
The LCM of 10 and 14 is calculated by listing the multiples of each number until we find a common multiple.
Multiples of 10 are 10, 20, 30, 40, 50, … and multiples of 14 are 14, 28, 42, 56, 70, ….
The smallest multiple they have in common is 70.
Therefore, you must purchase 7 packages of hamburger patties (since 7 × 10 = 70) and 5 packages of rolls (since 5 × 14 = 70) to have an equal number of 70 hamburgers and 70 rolls.