One half of the birds at the pet store are yellow . Tara buys one of the yellow birds. Then one third of the birds at the store are yellow. How many yellow birds were at the pet store before Tara bought one ?

If there were x birds, then

x/2 - 1 = 1/3 (x-1)
x = 4

So, there were originally 4 birds and 2 yellows.

After the sale, there was 1 yellow of 3 birds left.

So, answer the question.

Or, to eliminate one step, consider making x the number of yellow birds.

x - 1 = 1/3 (2x-1)
x = 2

To find the number of yellow birds at the pet store before Tara bought one, let's use algebra. Let's assume the total number of birds at the pet store initially was x.

According to the given information, half of the birds at the pet store are yellow, so there are x/2 yellow birds initially.

Tara buys one of the yellow birds, so now there are x/2 - 1 yellow birds left in the store.

It is also given that, after Tara buys one, one-third of the birds at the store are yellow. So we can write the equation:

(x/2 - 1) = x/3

Now, let's solve the equation for x:

Multiply both sides by 6 to eliminate the denominators:
6*(x/2 - 1) = 6*(x/3)
3x - 6 = 2x

Subtract 2x from both sides:
3x - 2x - 6 = 2x - 2x
x - 6 = 0

Add 6 to both sides:
x - 6 + 6 = 0 + 6
x = 6

Therefore, the initial total number of birds at the pet store was 6. Since half of them are yellow, there were 6/2 = 3 yellow birds at the pet store before Tara bought one.