A charging station can only charge cell phones and laptops. Cell phones use approximately $3\frac{J}{s}$ when charging, and laptops use approximately $40\frac{J}{s}$ when charging. Which of the following equations represents the relationship between the number of cell phones, $c$ , and the number of laptops, $l$ , that could be charging when the station's output is exactly $160\frac{J}{s}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $c=-40l+160$ $\newline$ (B) $c=-\frac{40}{3}l+\frac{160}{3}$ $\newline$ (C) $c=-3l+160$ $\newline$ (D) $c=-\frac{3}{40}l+\frac{160}{40}$

Full solution

Q. A charging station can only charge cell phones and laptops. Cell phones use approximately

3\frac{J}{s}

when charging, and laptops use approximately

40\frac{J}{s}

when charging. Which of the following equations represents the relationship between the number of cell phones,

c

, and the number of laptops,

l

, that could be charging when the station's output is exactly

160\frac{J}{s}

\newline

Choose

1

answer:

\newline

(A)

c=-40l+160

\newline

(B)

c=-\frac{40}{3}l+\frac{160}{3}

\newline

(C)

c=-3l+160

\newline

(D)

c=-\frac{3}{40}l+\frac{160}{40}

Define Total Power Output: Let's denote the total power used by cell phones as $P_c$ and the total power used by laptops as $P_l$ . The total power output of the station is $160\,\text{J}/\text{s}$ . We can write the equation for the total power output as: $\newline$ $P_c + P_l = 160$
Express Power in Terms of Devices: Now, let's express $P_c$ and $P_l$ in terms of $c$ and $l$ , respectively. Since each cell phone uses $3\frac{J}{s}$ , the total power used by $c$ cell phones is $3c$ . Similarly, since each laptop uses $40\frac{J}{s}$ , the total power used by $l$ laptops is $40l$ . We can now rewrite the equation as: $\newline$ $P_l$ $0$
Solve for Cell Phones Power: To find the equation that represents the relationship between $c$ and $l$ , we need to solve for $c$ . We can do this by subtracting $40l$ from both sides of the equation: $\newline$ $3c = 160 - 40l$
Divide to Find Cell Phones: Now, we divide both sides of the equation by $3$ to solve for $c$ : $\newline$ $c = \frac{160 - 40l}{3}$
Simplify the Equation: Simplify the equation by distributing the division across the terms in the numerator: $c = \frac{160}{3} - \frac{40l}{3}$
Simplify the Equation: Simplify the equation by distributing the division across the terms in the numerator: $c = \frac{160}{3} - \frac{40l}{3}$ The simplified equation is now in the form of $c$ in terms of $l$ , which matches one of the answer choices: $c = -\left(\frac{40}{3}\right)l + \left(\frac{160}{3}\right)$