One half of the birds at the pet store was yellow. Tara buys one of the yellow birds. The one third of the birds at the store are yellow. How many yellow birds were at the store before Tara brought one ?
x/2 - 1 = (x-1)/3
x = 4
half of 4 is 2 yellows to start with
less 1, leaves 1 yellow of 3 birds left
Let's assume the total number of birds at the pet store before Tara bought one as x.
According to the first statement, half of the birds at the store are yellow. So the number of yellow birds before Tara bought one is (1/2)x.
According to the second statement, one third of the birds at the store are yellow. So, (1/3)x birds are yellow.
Since both statements refer to the same situation, we can equate them:
(1/2)x = (1/3)x
To solve for x, we'll use basic algebra:
Multiply both sides of the equation by 6 (the least common multiple of 2 and 3):
6 * (1/2)x = 6 * (1/3)x
3x = 2x
Subtract 2x from both sides:
3x - 2x = 2x - 2x
x = 0
Therefore, before Tara bought one, there were 0 yellow birds at the store.
To find the number of yellow birds at the store before Tara bought one, we need to use the information given in the question.
Let's say the total number of birds at the store is 'x'.
According to the first statement, one-half of the birds at the pet store were yellow. This means there were (1/2)*x yellow birds at the store.
According to the second statement, one-third of the birds at the store are yellow. This implies that (1/3)*x yellow birds were at the store.
Since we know that Tara bought one of the yellow birds, we can subtract 1 from the total number of yellow birds at the store.
So, we have the equation:
(1/3)*x - 1 = (1/2)*x
To solve this equation, let's multiply each term by 6 to get rid of the denominators:
2x - 6 = 3x
Now, subtract 2x from both sides of the equation:
-x - 6 = 0
Add 6 to both sides:
-x = 6
Multiply by -1 to solve for 'x':
x = -6
To solve for 'x', we must have a positive number of birds at the store, so this equation does not have a valid solution.