Question
Jordan and Jane each bought a pack of cookies to eat before going on a strict diet for wrestling season. The number of cookies Jordan has left after x days is modeled by y=30−5x
, while the number of cookies Jane has left is modeled by y=24−3x
. How many days will it take for them to have the same number of cookies left?(1 point)
days
, while the number of cookies Jane has left is modeled by y=24−3x
. How many days will it take for them to have the same number of cookies left?(1 point)
days
Answers
GPT-4o mini
To find out how many days it will take for Jordan and Jane to have the same number of cookies left, we need to set their equations equal to each other:
For Jordan:
\[ y = 30 - 5x \]
For Jane:
\[ y = 24 - 3x \]
Setting the equations equal to each other:
\[ 30 - 5x = 24 - 3x \]
Now, let's solve for \( x \):
1. Add \( 5x \) to both sides:
\[ 30 = 24 - 3x + 5x \]
2. Simplify the equation:
\[ 30 = 24 + 2x \]
3. Subtract \( 24 \) from both sides:
\[ 30 - 24 = 2x \]
\[ 6 = 2x \]
4. Divide by \( 2 \):
\[ x = 3 \]
So, it will take **3 days** for Jordan and Jane to have the same number of cookies left.
\[
\text{Answer: } 3 \text{ days}
\]
For Jordan:
\[ y = 30 - 5x \]
For Jane:
\[ y = 24 - 3x \]
Setting the equations equal to each other:
\[ 30 - 5x = 24 - 3x \]
Now, let's solve for \( x \):
1. Add \( 5x \) to both sides:
\[ 30 = 24 - 3x + 5x \]
2. Simplify the equation:
\[ 30 = 24 + 2x \]
3. Subtract \( 24 \) from both sides:
\[ 30 - 24 = 2x \]
\[ 6 = 2x \]
4. Divide by \( 2 \):
\[ x = 3 \]
So, it will take **3 days** for Jordan and Jane to have the same number of cookies left.
\[
\text{Answer: } 3 \text{ days}
\]