Chapter SH, Problem 2.5MPS

(a)

To determine

To find:The equation could the art teacher use tofind the number.

Answer to Problem 2.5MPS

The equation could the art teacher use tofind the number is $x-4m-3=0$ and $x-5m+6=0$ .

Explanation of Solution

Given information:The given information is:

Sarahhas $3$ more than $4$ times a certain mystery number,

Jasminehas $9$ less than $5$ times the mystery number.

Calculation:

Let the mystery number is $m$ , Sarah is $x$ .

Now,

Sarahhas $3$ more than $4$ times a certain mystery number,

Sarahhas: $4m+3$

  $\begin{array}{l}x=4m+3\\ x-4m-3=0\end{array}$

Jasminehasthe same amount of beads as Sarah but said $9$ less than $5$ times the mystery number.

Jasminehas: $\left(5m+3\right)-9$

  $\begin{array}{l}x=\left(5m+3\right)-9\\ x-5m+6=0\end{array}$

Therefore,the equation could the art teacher use tofind the numberis $x-4m-3=0$ and $x-5m+6=0$ .

(b)

To determine

To find:The mystery number.

Answer to Problem 2.5MPS

The mystery number is $m=9$ .

Explanation of Solution

Given information: The given information is:

Sarahhas $3$ more than $4$ times a certain mystery number,

Jasminehas $9$ less than $5$ times the mystery number.

Calculation:

By above equation:

  $x-4m-3=0\mathrm{..........}\left(1\right)$

  $x-5m+6=0\mathrm{...........}\left(2\right)$

Now, subtract the above equation:

  $\begin{array}{l}x-4m-3=0\\ \frac{x-5m+6=0}{m-9=0}\end{array}$

  $\begin{array}{l}m-9=0\\ m=9\end{array}$

Therefore,themystery number is $m=9$ .

(c)

To determine

To find:The how many beads does each girl have.

Answer to Problem 2.5MPS

TheSarahhas and Jasminehas $39$ beads.

Explanation of Solution

Given information: The given information is:

Mystery number is $m=9$ .

Sarahhas $3$ more than $4$ times a certain mystery number,

Jasminehas $9$ less than $5$ times the mystery number.

Calculation:

From the above equation:

Sarahhas $3$ more than $4$ times a certain mystery number,

Sarahhas: $4m+3$

So, theSarahhas: $4m+3$

  $4m+3=4\times 9+3=39$

Jasminehasthe same amount of beads as Sarah but said $9$ less than $5$ times the mystery number.

So, the Jasminehas: $\left(5m+3\right)-9$

  $\left(5m+3\right)-9=\left(5\times \left(9\right)+3\right)-9=39$

Therefore,the Sarahhas and Jasminehas $39$ beads.