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A piece of glass with an initial temperature of
99^(@)C is cooled at a rate of
3.5^(@)C per minute. At the same time, a piece of copper with an initial temperature of
0^(@)C is heated at
2.5^(@)C per minute. Which of the following systems of equations can be used to solve for the temperature,
T, in degrees Celsius, and the time,
m, in minutes, when the glass and copper reach the same temperatures?

A piece of glass with an initial temperature of $99^{\circ} \mathrm{C}$ is cooled at a rate of $3.5^{\circ} \mathrm{C}$ per minute. At the same time, a piece of copper with an initial temperature of $0^{\circ} \mathrm{C}$ is heated at $2.5^{\circ} \mathrm{C}$ per minute. Which of the following systems of equations can be used to solve for the temperature, $T$ , in degrees Celsius, and the time, $m$ , in minutes, when the glass and copper reach the same temperatures?

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Solve equations with variables on both sides: word problems

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Q. A piece of glass with an initial temperature of

99^{\circ} \mathrm{C}

is cooled at a rate of

3.5^{\circ} \mathrm{C}

per minute. At the same time, a piece of copper with an initial temperature of

0^{\circ} \mathrm{C}

is heated at

2.5^{\circ} \mathrm{C}

per minute. Which of the following systems of equations can be used to solve for the temperature,

T

, in degrees Celsius, and the time,

m

, in minutes, when the glass and copper reach the same temperatures?

Define Glass Temperature Equation: Define the equations for the temperature of the glass and copper over time. $\newline$ The temperature of the glass as it cools can be represented by the equation $T_g = 99 - 3.5m$ , where $T_g$ is the temperature of the glass in degrees Celsius and $m$ is the time in minutes.
Define Copper Temperature Equation: Define the equation for the temperature of the copper as it heats up. $\newline$ The temperature of the copper as it heats can be represented by the equation $T_c = 0 + 2.5m$ , where $T_c$ is the temperature of the copper in degrees Celsius and $m$ is the time in minutes.
Set Equations Equal: Set the two equations equal to each other to find when the temperatures are the same. $\newline$ To find the time $m$ when the glass and copper have the same temperature, we set $T_g$ equal to $T_c$ : $\newline$ $99 - 3.5m = 0 + 2.5m$
Combine Equations: Combine the equations into a system of equations. $\newline$ The system of equations that can be used to solve for the temperature $T$ and the time $m$ when the glass and copper reach the same temperature is: $\newline$ $T = 99 - 3.5m$ $\newline$ $T = 0 + 2.5m$

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