Q. 11 PT - Algebra 1

Question

The ${\mathbf{8}}^{\mathbf{t}\mathbf{h}}$  grade science class is going to the zoo. The class can spend up to $\mathit{\backslash (}\mathbf{300}$ admission.

Zoo Admission
Visitor	Cost
Student	$\mathbf{\backslash )}\mathbf{8}$
Adult	$\mathbf{\$}\mathbf{10}$

a. Write an inequality for this situation.

b. If there are   students in the class and   adults will attend for every   student, how much will admission be?

Step-by-Step Solution

Answer

1. The inequality for this situation is $\mathbf{8}\mathit{x}\mathbf{+}\mathbf{10}\mathit{y}\mathbf{\le }\mathbf{300}$.
2. The number of admissions will be $\mathbf{36}$. 

Step1. Observe the given table.

The given table is:

Zoo Admission
Visitor	Cost
Student	$\$8$
Adult	$\$10$

From the given table, it can be noticed that cost of $1$ admission of the student is   and the cost of $1$ admission of $1$ the adult is $\$10$.

Step 2. Write an inequality for this situation.

The inequality for the given situation is:

Let $x$, $y$ be the number of students and adults respectively.

The cost of 1 admission of the student is  and cost of admission of 1 adult is $\$10$.

Therefore, the cost of admission of $x$ students and $y$ adults is given by $8x+10y$.

The class can spend up to $\$300$ admission. Therefore, that implies:

$8x+10y\le 300$

Therefore, the inequality for this situation is $8x+10y\le 300$.

Step 3. Calculation

It is given that the cost of 1 admission of the student is   and cost of 1 admission of 1 adult is $\$10$.

It is also given that there are students in the class and 1 adult will attend for every $8$ student.

If there are $8$ students, $1$ the adult will be there.

If there is $1$ a student, $\frac{1}{8}$ the adult will be there.

Therefore, if there are $32$ students, then:

$\frac{1}{8}\times 32\text{\hspace{0.17em}adults}=4\text{ adults}$

Therefore, the number of admissions is given by:

$32+4=36$

Therefore, the number of admissions will be $36$.