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?

Answer 1

To find out how many days it will take for Jordan and Jane to have the same number of cookies left, we can set their equations equal to each other.

The equations are:
- For Jordan: \( y = 30 - 5x \)
- For Jane: \( y = 24 - 3x \)

Setting these equal to each other:
\[
30 - 5x = 24 - 3x
\]

Now, we will solve for \( x \):

1. First, let's add \( 5x \) to both sides:
\[
30 = 24 - 3x + 5x
\]
\[
30 = 24 + 2x
\]

2. Next, subtract \( 24 \) from both sides:
\[
30 - 24 = 2x
\]
\[
6 = 2x
\]

3. Now, divide both sides by \( 2 \):
\[
x = 3
\]

So, it will take Jordan and Jane **3 days** to have the same number of cookies left.

To verify, we can substitute \( x = 3 \) back into both equations:

- For Jordan:
\[
y = 30 - 5(3) = 30 - 15 = 15
\]

- For Jane:
\[
y = 24 - 3(3) = 24 - 9 = 15
\]

Both equations give \( y = 15 \), confirming that they will indeed have the same number of cookies left after **3 days**.