(a) To find the unit rate using the given ratio of 6 blueberries to 14 strawberries, we can set up a proportion and solve for one unit of blueberries.
Let's set up the proportion:
6 blueberries / 14 strawberries = x blueberries / y strawberries
To find the first unit rate, we can set y (strawberries) as one and solve for x (blueberries):
6 / 14 = x / 1
Cross multiplying, we get:
14x = 6 * 1
14x = 6
Dividing both sides by 14:
x = 6/14
Simplifying the fraction, we get:
x = 3/7
So, the first unit rate is "3 blueberries for each 7 strawberries."
Now, let's find the second unit rate. We can set x (blueberries) as one and solve for y (strawberries):
6 / 14 = 1 / y
Cross multiplying, we get:
6y = 14 * 1
6y = 14
Dividing both sides by 6:
y = 14/6
Simplifying the fraction, we get:
y = 7/3
So, the second unit rate is "6 blueberries for each 7/3 strawberries."
(b) To determine the number of blueberries needed if 21 strawberries are used, we can use the ratio provided and set up a proportion:
6 blueberries / 14 strawberries = x blueberries / 21 strawberries
Cross multiplying, we get:
14x = 6 * 21
14x = 126
Dividing both sides by 14:
x = 126 / 14
Simplifying the fraction, we get:
x = 9
Therefore, 9 blueberries are needed if 21 strawberries are used.