Chapter 3.2, Problem 62SR

(a)

To determine

To find: the equation that can be used to show money is left in the activities account.

Answer to Problem 62SR

The equation is $y=500-25x$ .

Explanation of Solution

Given:

Putnam high school book club $\$25$ take to buy snacks and materials for each meeting.

There is $\$350$ left in the activities account.

Concept used:

The difference is that a solution to the inequality is not the drawn line but coordinate plane that satisfy the inequality.

The boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ .

Calculation:

Consider a Putnam high school book club $\$25$ take to buy snacks and materials for each meeting.

The total number of $6$ meeting then the total amount has to be taken to buy snacks and material is:

  $25\times 6=150$ .

After $6$ meeting the remaining amount is $\$350$ which means before $6$ meeting the total amount was:

  $\$150+\$350=\$500$ .

Let $y$ is the amount of each $x$ meeting.

Then the equation is,

  $y=500-25x$ .

Hence, the equation is $y=500-25x$ .

(b)

To determine

To find: the amount of money that was originally in the account.

Answer to Problem 62SR

The originally amount was $\$500$ .

Explanation of Solution

Given:

Putnam high school book club $\$25$ take to buy snacks and materials for each meeting.

There is $\$350$ left in the activities account.

Concept used:

The difference is that a solution to the inequality is not the drawn line but coordinate plane that satisfy the inequality.

The boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ .

Calculation:

The total amount in the account was as follows:

  $\begin{array}{l}6\text{ meeting amount+after }6\text{ meeting remaining amount=}\$150+\$350.\\ \Rightarrow \$500.\end{array}$

Hence, the originally amount was $\$500$ .

(c)

To determine

To find: the number of meetings after there will be no money left in the activities account.

Answer to Problem 62SR

The meeting when there is no money left is $20$ .

Explanation of Solution

Given:

Putnam high school book club $\$25$ take to buy snacks and materials for each meeting.

There is $\$350$ left in the activities account.

Concept used:

The difference is that a solution to the inequality is not the drawn line but coordinate plane that satisfy the inequality.

The boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ .

Calculation:

After $x$ number of meeting there is no money left in the account.

So, substitute the value of:

  $\begin{array}{l}y=0.\\ y=500-25x.\end{array}$

Simplify it as follows.

  $\begin{array}{l}0=500-25x.\\ 25x=500.\\ x=20.\end{array}$

Hence, the meeting when there is no money left is $20$ .