There was a surge in math club membership after the fun Halloween party. When the principal asked Mrs. Germain how many students were currently in the club, she replied, "Three times our number plus a third of our number plus a fourth of our number plus you and me is two hundred sixty."
The principal smiled and nodded, then added, "If you can pick up another eight students before your Christmas party you will have exactly 10% of the student body involved in the club."
How many students are enrolled in the math club? How many students are in the school?
Be sure to explain how you found your answer.
Please help thanks
Simply translate the English into Math, (Mathematics is a language)
"Three times our number plus a third of our number plus a fourth of our number plus you and me is two hundred sixty."
let "our number" be x
3x + (1/3)x + (1/4)x + 1 + 1 = 260
3x + (1/3)x + (1/4)x = 258
x(3 + 1/3 + 1/4) = 258
(43/12)x = 258
x = 258(12/43) = 72
so .....
2nd part:
so after picking up 8 more, they would have 80 in the club
If that is 10% of the student body, how many students were there in total ???
Please do not keep spamming this board with this post. Be patient until a math tutor can help you.
To find out how many students are enrolled in the math club, we can solve the given equation:
"Three times our number plus a third of our number plus a fourth of our number plus you and me is two hundred sixty."
Let's break down the equation:
Let's assume the number of students in the math club is 'x'.
Three times our number: 3x
A third of our number: (1/3)x
A fourth of our number: (1/4)x
You and me: 2 (since it represents the principal and Mrs. Germain)
Putting it all together, we have the equation:
3x + (1/3)x + (1/4)x + 2 = 260
To solve this equation, we need to combine like terms:
(12/12)x + (4/12)x + (3/12)x + 2 = 260
(19/12)x + 2 = 260
Now, isolate the variable:
(19/12)x = 260 - 2
(19/12)x = 258
To solve for 'x', we can multiply both sides by the reciprocal of (19/12), which is (12/19):
x = (258)(12/19)
x ≈ 163.263
Since we can't have a fractional number of students, we can round off the answer to the nearest whole number. So, there are approximately 163 students in the math club.
To find out how many students are in the school, we can use the second piece of information given:
"If you can pick up another eight students before your Christmas party, you will have exactly 10% of the student body involved in the club."
This tells us that the math club will have 10% of the student body when the total number of students increases by 8. So, the number of students in the school is:
Total students = (Math club students / 10%) * 100%
Total students = (163 / 10%) * 100%
Total students = 1630
Therefore, there are approximately 163 students enrolled in the math club, and the total number of students in the school is approximately 1630.