Nancy and Ezra are both making bracelets with beads. Nancy's bracelet starts with 24 beads and she adds 2 more every minute. Ezra is taking apart his bracelet. Ezra's bracelet starts with 48 beads and he removes 4 every minute. Is there a time when their bracelets will have the same number of beads?

Question

The equation below represents the number of beads, y, that Ezra has on his bracelet after x minutes. Use the equation to complete the table with the number of beads on Ezra bracelet for the given number of minutes. You can solve on paper and then enter your answer on Zearn.
y=48−4x

Minutes (x) Beads (y)
2
4
8
Nice!
Next, graph the points you just found on the coordinate plane to show the relationship between the number of minutes that have passed and the number of beads remaining on Ezra’s bracelet.
Minutes (x) Beads (y)
2 40
4 32
8 16
You got it!
Next, consider Nancy. The equation below represents the number of beads, y, that Nancy has on her bracelet after x minutes. Use the equation to complete the table with the number of beads on Nancy’s bracelet for the given number of minutes. You can solve on paper and then enter your answer on Zearn.
y=24+2x

Minutes (x) Beads (y)
2
4
6

Answer 1

To calculate the number of beads on Nancy's bracelet for the specified minutes using the equation \(y = 24 + 2x\), we can plug in the values for \(x\) (the number of minutes) into the equation.

1. For \(x = 2\): \[ y = 24 + 2(2) = 24 + 4 = 28 \]

2. For \(x = 4\): \[ y = 24 + 2(4) = 24 + 8 = 32 \]

3. For \(x = 6\): \[ y = 24 + 2(6) = 24 + 12 = 36 \]

Now, we can summarize the results in a table for Nancy's bracelet:

| Minutes (x) | Beads (y) | |-------------|-----------| | 2 | 28 | | 4 | 32 | | 6 | 36 |

Now, we can find out if there is a time when Nancy and Ezra have the same number of beads:

1. Nancy's beads after \(x\) minutes: \(y = 24 + 2x\)
2. Ezra's beads after \(x\) minutes: \(y = 48 - 4x\)

To find the time \(x\) when their bracelets have the same number of beads, we can set the two equations equal to each other:

\[ 24 + 2x = 48 - 4x \]

Now solve for \(x\):

\[ 2x + 4x = 48 - 24 \] \[ 6x = 24 \] \[ x = 4 \]

At \(x = 4\) minutes, both Nancy and Ezra will have the same number of beads.

To find out how many beads they each have at that time: For Nancy: \[ y = 24 + 2(4) = 24 + 8 = 32 \]

For Ezra: \[ y = 48 - 4(4) = 48 - 16 = 32 \]

So both Nancy and Ezra will have 32 beads after 4 minutes.