Plugging In: Invisible Plugging In - Fractions

Jane, John, and Joanne share an apartment. Jane spends half of her salary on rent. John and Joanne spend one-third and one-fourth of their salaries, respectively, on rent. If the rent amount paid by each of the three residents is the same, what fraction of their combined salaries goes towards paying rent?

Incorrect. [[snippet]]

Incorrect. [[snippet]]

Incorrect. [[snippet]] Did you take the average of $$\frac{1}{2}$$, $$\frac{1}{3}$$, and $$\frac{1}{4}$$? You cannot assume that all three earn the same since all three pay the same rent and that amount constitutes different fractions of their individual salaries.

Correct. [[snippet]] __Plug In__ a good number for the rent _each_ of the three friends pays, such as $2. The total rent is then $$3 \times $2$$, or $6. Next, calculate the salary for each of the three. Since Jane spends half of her salary on rent and the rent she pays is $2, Jane earns $4 (half of $4 is $2). The $2 John spends on rent constitutes a third of his salary, so he earns $6 (a third of $6 is $2), and Joanne spends one-fourth of her salary on rent, so she earns $8 ($2 is one-fourth of $8). The total income of all three is therefore $$ $4 + $6 + $8= $18$$. The fraction of their salaries going towards rent is the total rent ($6) divided by the total income ($18): >$$\displaystyle \frac{6}{18}=\frac{1}{3}$$.

Incorrect. [[snippet]]

$$\frac{1}{9}$$

$$\frac{1}{6}$$

$$\frac{5}{12}$$

$$\frac{1}{3}$$

$$\frac{1}{12}$$