The Pizza Problem
A group of friends decide to meet for pizza, and one friend calls ahead to order the pies. However, three people in the group do not show up at the pizza parlor. The friends who do show up figure that they each add $3 to their original share, to cover the bill, which totals $70. How many friends eat pizza?
Solution - The Pizza Problem
Let f = the number of friends expected to eat pizza
Alternate Solution - The Pizza Problem
Another way we can look at it is this way...
Let f = the number of friends expected to eat pizza.
The only possible values for f and f - 3 must be divisors of 70 (1, 2, 5, 7, 10, 14, 35, and 70).
The only two numbers in the set that differ by 3 in the divisors are 7 and 10.
Therefore, we can see here that the solution in this case is 7 number of friends expected to eat pizza.
Let f = the number of friends expected to eat pizza.
The only possible values for f and f - 3 must be divisors of 70 (1, 2, 5, 7, 10, 14, 35, and 70).
The only two numbers in the set that differ by 3 in the divisors are 7 and 10.
Therefore, we can see here that the solution in this case is 7 number of friends expected to eat pizza.