Carrie and Luke drank 4/5 of a bottle of juice. Carrie drank half as much as Luke. What fraction of the juice did Carrie drink?
Answer given is 4/15
isn't it 2/5?
yes it would be 2/5
Step 1: Let's assume that the whole bottle of juice is represented by the fraction 1.
Step 2: Carrie and Luke together drank 4/5 of the bottle of juice.
Step 3: So, the amount of juice they drank together is 4/5 of 1, which is (4/5) x 1 = 4/5.
Step 4: Let's say the amount of juice Luke drank is represented by the fraction L.
Step 5: Since Carrie drank half as much as Luke, the amount of juice Carrie drank is represented by the fraction L/2.
Step 6: We know that Carrie and Luke together drank 4/5 of the bottle, so the sum of the amounts they drank should be equal to 4/5.
Step 7: Therefore, the equation is L + L/2 = 4/5.
Step 8: To solve the equation, let's first find a common denominator. The denominators are 1, 2, and 5. The least common multiple (LCM) of 1, 2, and 5 is 10.
Step 9: Multiply the equation by 10 to eliminate the denominators: (10L) + (10L/2) = (4/5) x 10.
Step 10: Simplify the equation: 10L + 5L = 8.
Step 11: Combine like terms: 15L = 8.
Step 12: Divide both sides of the equation by 15 to solve for L: L = 8/15.
Step 13: Now that we know L is equal to 8/15, we can find the amount of juice Carrie drank.
Step 14: Carrie drank half as much as Luke, so the amount of juice Carrie drank is (8/15) x (1/2) = 4/15.
Therefore, Carrie drank 4/15 of the bottle of juice.
To find out what fraction of the juice Carrie drank, we first need to determine how much juice Luke drank.
Let's assign a variable to represent the amount of juice in the bottle. For example, let x = total amount of juice.
According to the given information, both Carrie and Luke drank 4/5 of the bottle. So, the total amount they drank together is 4/5 of x.
We also know that Carrie drank half as much as Luke. Therefore, if we let y represent the amount of juice Luke drank, Carrie drank y/2.
Since the total amount they drank together is 4/5 of the bottle, we can write an equation:
y + y/2 = 4/5 x
To simplify this equation, we multiply both sides by 2 to get rid of the fraction in the equation:
2y + y = (4/5)x * 2
Combining like terms:
3y = (8/5)x
We want to find the fraction of juice Carrie drank, which is y/((4/5)x). So, we divide both sides of the equation by the total amount of juice in the bottle (x):
(3y/x) = (8/5)
Now, let's substitute the value we know: Carrie drank half as much as Luke, so y = 2y/2.
(3*(2y/2))/x = (8/5)
Simplify this equation:
(3y)/(2x) = (8/5)
Now, let's plug in y = 2y/2:
(3*(2y/2))/(2x) = (8/5)
Simplify by canceling the 2s:
(3y)/(x) = (8/5)
Since we want to find the fraction of juice Carrie drank, which is y/(4/5x), we can rearrange the equation:
y/(4/5x) = (8/5)
Divide both sides by (4/5x):
y = (8/5) * (4/5x)
Multiply the numerators and denominators together:
y = (32/25x)
Now that we have the expression for the amount of juice Luke drank (y), we can substitute it back into the fraction to find the fraction of juice Carrie drank:
Carrie drank y/2 = (32/25x)/2 = (32/25x) * (1/2)
Multiply the numerators and denominators:
Carrie drank 32/50x = 16/50x
Simplify the fraction:
Carrie drank 8/25x
Thus, the fraction of the juice that Carrie drank is 8/25.