Question

A student has a daily reading productivity level of 1 chapter while at a computer lab, 5 chapters while at a coffee shop, and 8 chapters while at a library. If 112 of the day is spent at a computer lab, 14 at a coffee shop, and 23 at a library, what is the total daily reading productivity level of the student? Write the solution as a mixed number or a fraction in lowest terms.

Answer 1

Answer:

$\textsf{Mixed number:}\quad 6\frac{2}{3}\; \sf chapters$

$\textsf{Fraction:}\quad \dfrac{20}{3}\;\sf chapters$

Step-by-step explanation:

To find the total daily reading productivity level, we need to calculate the weighted average based on the time spent at each location.

Let C be the number of chapters read at the computer lab.

Let S be the number of chapters read at the coffee shop.

Let L be the number of chapters read at the library.

The time spent at each location is given as:

• Computer lab: ¹/₁₂ of the day
• Coffee shop: ¹/₄ of the day
• Library: ²/₃ of the day

Now, we can set up the equation for the total daily reading productivity level:

$\textsf{Total productivity} = \dfrac{1}{12} \cdot C + \dfrac{1}{4} \cdot S + \dfrac{2}{3} \cdot L$

Given reading productivity levels:

• C = 1 chapter at the computer lab.
• S = 5 chapters at the coffee shop.
• L = 8 chapters at the library.

Substitute these values into the equation:

$\textsf{Total productivity} = \dfrac{1}{12} \cdot 1 + \dfrac{1}{4} \cdot 5 + \dfrac{2}{3} \cdot 8$

Solve:

$\begin{aligned}\textsf{Total productivity} &= \dfrac{1}{12} + \dfrac{5}{4}+ \dfrac{16}{3}\\\\&= \dfrac{1}{12} + \dfrac{5\cdot 3}{4\cdot 3}+ \dfrac{16\cdot 4}{3\cdot 4}\\\\&= \dfrac{1}{12} + \dfrac{15}{12}+ \dfrac{64}{12}\\\\&=\dfrac{1+15+64}{12}\\\\&=\dfrac{80}{12}\\\\&=\dfrac{80\div 4}{12\div 4}\\\\&=\dfrac{20}{3}\end{aligned}$

So, the total daily reading productivity level of the student is:

$\textsf{Mixed number:}\quad 6\frac{2}{3}\; \sf chapters$

$\textsf{Fraction:}\quad \dfrac{20}{3}\;\sf chapters$