28 students collected 12,374 soda can tabs. If some of the students collected one more tab each than the rest of the students, how many collected 441 and how many collected 442 tabs?
12,374 / 28 = 441.928571
0.928571 * 28 = 26 collected 442 tabs
Let's solve this problem step by step:
Step 1: Let's assume that the number of students who collected 441 tabs is A and the number of students who collected 442 tabs is B.
Step 2: We know that the total number of students is 28, so A + B = 28.
Step 3: We also know that the total number of soda can tabs collected by all the students is 12,374. Therefore, the total number of tabs collected by students who collected 441 tabs (A) and students who collected 442 tabs (B) can be represented as:
441A + 442B = 12,374.
Step 4: We have two equations now:
A + B = 28, and
441A + 442B = 12,374.
Step 5: Now we can solve these equations simultaneously to find the values of A and B.
Using the substitution method, we can rewrite the equation A + B = 28 as A = 28 - B.
Substituting this value of A in the second equation:
441(28 - B) + 442B = 12,374.
Expanding the equation:
12,348 - 441B + 442B = 12,374.
Combining like terms:
442B - 441B = 12,374 - 12,348.
B = 26.
Step 6: Now that we have B = 26, we can substitute this value in the equation A = 28 - B to find A:
A = 28 - 26,
A = 2.
Therefore, 2 students collected 441 tabs, and 26 students collected 442 tabs.