Question

jasmine
was the lead dancer for her dance troupe. She and the troupe's choreographer (also a troupe member) decided that they needed to have one more rehearsal before they performed.

Answer 1

The members in Jasmine's dance troupe is an illustration equivalent expressions.

The number of members in Jasmine's dance troupe is 62

Assume the number of dancers is n.

One third of the rest is:

$\mathbf{x = \frac{1}{3}(n - 2)}$

When she called three more, we have:

$\mathbf{x = \frac{1}{3}(n - 2) + 3}$

Expand

$\mathbf{x = \frac{n}{3} - \frac{2}{3} + 3}$

$\mathbf{x = \frac{n}{3} + \frac{-2 + 9}{3}}$

$\mathbf{x = \frac{n}{3} + \frac{7}{3}}$

The remaining dancers (r) are:

$\mathbf{r = n- \frac{n}{3} - \frac{7}{3}}$

$\mathbf{r = \frac{3n - n}{3} - \frac{7}{3}}$

$\mathbf{r = \frac{2n}{3} - \frac{7}{3}}$

$\mathbf{r = \frac{2n - 7}{3}}$

When two-fifth of the remaining dancers are added, we have:

$\mathbf{x = \frac{n}{3} + \frac{7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}$

$\mathbf{x = \frac{n+7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}$

$\mathbf{x = \frac{n+7}{3} + \frac{4n - 14}{15}}$

Take LCM

$\mathbf{x = \frac{5n + 35 + 4n - 14}{15}}$

$\mathbf{x = \frac{9n + 21}{15}}$

$\mathbf{x = \frac{3n + 7}{5}}$

When she called one more dancer, we have:

$\mathbf{x = \frac{3n + 7}{5} + 1}$

$\mathbf{x = \frac{3n + 7+5}{5}}$

$\mathbf{x = \frac{3n + 12}{5}}$

The remaining of the dancer is:

$\mathbf{r = n - \frac{3n + 12}{5}}$

$\mathbf{r = \frac{5n - 3n + 12}{5}}$

$\mathbf{r = \frac{2n + 12}{5}}$

When three-fourth are added, we have:

$\mathbf{x = \frac{3n + 12}{5} +\frac{3}{4} \times \frac{2n + 12}{5}}$

$\mathbf{x = \frac{3n + 12}{5} + \frac{6n + 36}{20}}$

Take LCM

$\mathbf{x = \frac{12n + 48+6n + 36}{20}}$

$\mathbf{x = \frac{18n +84}{20}}$

When the last two members are added, we have:

$\mathbf{n = \frac{18n +84}{20} + 2}$

$\mathbf{n = \frac{18n +84+40}{20} }$

$\mathbf{n = \frac{18n +124}{20} }$

Multiply through by 20

$\mathbf{20n = 18n +124}$

Collect like terms

$\mathbf{20n - 18n =124}$

$\mathbf{2n =124}$

Divide both sides by 2

$\mathbf{n =62}$

Hence, the number of members in Jasmine's dance troupe is 62

Read more about equivalent expressions at:

https://brainly.com/question/15715866