There 100 people sharing 100 buns in a party. Each adult can take 3 buns while three kids have to share 1 bun. Find the number of adults and kids in the party.

a+c = 100

3a + c/3 = 100
solve as usual

a + b = c

like my post above!

hi

hi
99764

Let's assume the number of adults in the party is "x" and the number of kids is "y". We can use algebraic equations to solve this problem.

According to the problem, there are 100 people in total. So the first equation we can write is:
x + y = 100 -- equation 1

Next, we know that each adult can take 3 buns, and there are x adults. So the total number of buns taken by adults will be 3x.

We also know that three kids have to share 1 bun. So the total number of buns taken by kids will be 1/3 of the number of kids, which means (1/3) * y.

The total number of buns taken by adults and kids should equal the total number of buns available, which is 100. Therefore, we can write the second equation as:
3x + (1/3)y = 100 -- equation 2

Now we have a system of two equations (equation 1 and equation 2) with two variables (x and y). We can solve this system of equations simultaneously to find the values of x and y.

Multiplying equation 1 by 3, we get:

3x + 3y = 300 -- equation 3

Now we have two equations:
3x + (1/3)y = 100 -- equation 2
3x + 3y = 300 -- equation 3

Subtracting equation 2 from equation 3, we eliminate the variable x:

(3x + 3y) - (3x + (1/3)y) = 300 - 100
(3x - 3x) + (3y - (1/3)y) = 200
(0) + (8/3)y = 200
(8/3)y = 200

To isolate y, we can multiply both sides by (3/8):

y = (200 * 3) / 8
y = 600 / 8
y = 75

So there are 75 kids in the party.

Substituting the value of y back into equation 1, we can find x:

x + 75 = 100
x = 100 - 75
x = 25

Therefore, there are 25 adults in the party.

So the answer is there are 25 adults and 75 kids in the party.