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

The equation below represents the number of beads, y, that Audrina has on her bracelet after x minutes. Use the equation to complete the table with the number of beads on Audrina 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
Good work!
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 Audrina’s bracelet.
Minutes (x) Beads (y)
2 40
4 32
8 16
Nice!
Next, consider Greg. The equation below represents the number of beads, y, that Greg has on his bracelet after x minutes. Use the equation to complete the table with the number of beads on Greg’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

1 answer

To determine the number of beads Audrina has on her bracelet after the specified minutes using the equation \( y = 48 - 4x \):

  1. For \( x = 2 \): \[ y = 48 - 4(2) = 48 - 8 = 40 \]

  2. For \( x = 4 \): \[ y = 48 - 4(4) = 48 - 16 = 32 \]

  3. For \( x = 8 \): \[ y = 48 - 4(8) = 48 - 32 = 16 \]

So, the completed table for Audrina's beads is:

| Minutes (x) | Beads (y) | |-------------|-----------| | 2 | 40 | | 4 | 32 | | 8 | 16 |

Now, let's calculate the number of beads Greg has using the equation \( y = 24 + 2x \):

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

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

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

So, the completed table for Greg's beads is:

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

Now, to determine if there is a time when Greg's and Audrina's bracelets will have the same number of beads, we need to set their equations equal:

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

Solving for \( x \):

  1. Add \( 4x \) to both sides: \[ 24 + 2x + 4x = 48 \] \[ 24 + 6x = 48 \]

  2. Subtract 24 from both sides: \[ 6x = 24 \]

  3. Divide by 6: \[ x = 4 \]

At \( x = 4 \), both have the same number of beads:

  • For Audrina: \( y = 48 - 4(4) = 32 \)
  • For Greg: \( y = 24 + 2(4) = 32 \)

Thus, yes, there is a time when both bracelets will have the same number of beads, and that is at 4 minutes when they both have 32 beads.