Mrs.Ryan gave her class cupcakes. She gave half the class yellow, a third of her class chocolate and the remaining students vanilla. If 5 students got vanillia how mny students are in the class? How many got yellow? Chocolate?
1-(1/2+1/3)=?
That will tell you the fraction remaining of kids in her class. They all got vanilla. Try to go from there. Post your answer if you want us to check it.
Let's assume the total number of students in Mrs. Ryan's class is "x".
If half the class got yellow cupcakes, then the number of students who got yellow cupcakes is (1/2) * x.
If a third of the class got chocolate cupcakes, then the number of students who got chocolate cupcakes is (1/3) * x.
Since 5 students got vanilla cupcakes, the remaining students who got vanilla cupcakes can be calculated as:
x - [(1/2) * x + (1/3) * x + 5].
We can now solve the equation to find the value of "x".
(1/2) * x + (1/3) * x + 5 = x.
Multiplying through by 6 to clear the denominators, we have:
3x + 2x + 30 = 6x.
Combining like terms gives:
5x + 30 = 6x.
Subtracting 5x from both sides, we have:
30 = x.
Therefore, there are 30 students in Mrs. Ryan's class.
To find the number of students who got yellow cupcakes, we substitute the value of "x" into the equation (1/2) * x:
(1/2) * 30 = 15 students.
To find the number of students who got chocolate cupcakes, we substitute the value of "x" into the equation (1/3) * x:
(1/3) * 30 = 10 students.
So, 15 students got yellow cupcakes, and 10 students got chocolate cupcakes.
To find the total number of students in the class, we need to determine the least common multiple (LCM) of 2 and 3, since the cupcakes were distributed among half of the class (which is half of a whole number) and a third of the class (which is one-third of a whole number).
The LCM of 2 and 3 is 6. Therefore, we can conclude that there are 6 students in the class.
Since 5 students received vanilla cupcakes, which is the remaining group after yellow and chocolate cupcakes were distributed, we can subtract 5 from the total number of students in the class to find the number of students who got yellow and chocolate cupcakes.
6 - 5 = 1
Thus, 1 student got yellow cupcakes and 1 student got chocolate cupcakes.