Q6. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Jason is playing games at a family fun center. So far he has won 38 prize tickets. How many more tickets would he need to win to place him in the gold prize category?

Number of Tickets	Prize Category
$1-20$	bronze
$21-40$	silver
$41-60$	gold
$61-80$	platinum

 

F $2\le t\le 22$

G $3\le t\le 22$

H $1\le t\le 20$

J $3\le t\le 20$

Step-by-Step Solution

Answer

The number of tickets that he would need to win to place him in the gold prize category is such that  $\mathbf{3}\mathbf{\le }\mathit{t}\mathbf{\le }\mathbf{22}$. Therefore, option G is correct.

Step1. Given

It is given that Jason has won   prize tickets

Step2. Write the inequality for the given problem.

Let $t$ be the number of more that he would need to win to place him in the gold prize category.

Therefore, the number of prize tickets that he has won is $38+t$.

To place him in the gold prize category, the number of tickets must lie between 41and 60.

Therefore, the inequality for the given problem is:

$41\le 38+t\le 60$

Step3. Solve the inequality 41 ≤ 38 + t ≤ 60 .

Solve the inequality $41\le 38+t\le 60$.

Therefore, it is obtained that:

  $$\begin{gathered} 41\le 38+t\le 60 \\ 41-38\le 38+t-38\le 60-38 \\ 3\le t+38-38\le 22 \\ 3\le t\le 22 \end{gathered}$$

Therefore, the number of tickets that he would need to win to place him in the gold prize category is such that $3\le t\le 22$. Therefore, option G is correct.