$4$ . The table shows the amount it costs to rock climb at an indoor rock climbing facility, based on the number of hours. What is the rule to find the amount charged to rock climb for $x$ hours? (Example $4$ ) $\newline$ Identify Structure Determine how the next term in each sequence $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline Time $(x)$ & Amount (\$) \\$\newline$\hline $1$ & $13$ \\$\newline$\hline $2$ & $21$ \\$\newline$\hline $3$ & $29$ \\$\newline$\hline $4$ & $37$ \\$\newline$\hline $ 5 x $ & $ 45= $ \\$\newline$\hline$\newline$\end{tabular}$\newline$can be found. Then find the next two terms in the sequence.

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Grade 6

Divide fractions and mixed numbers: word problems

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4

. The table shows the amount it costs to rock climb at an indoor rock climbing facility, based on the number of hours. What is the rule to find the amount charged to rock climb for

x

hours? (Example

4

)

\newline

Identify Structure Determine how the next term in each sequence

\newline

\begin{tabular}{|c|c|}

\newline

\hline Time

(x)

& Amount (\$) \\$\newline$\hline $1$ & $13$ \\$\newline$\hline $2$ & $21$ \\$\newline$\hline $3$ & $29$ \\$\newline$\hline $4$ & $37$ \\$\newline$\hline $ 5 x $ & $ 45= $ \\$\newline$\hline$\newline$\end{tabular}$\newline$can be found. Then find the next two terms in the sequence.

Identify Pattern: Identify the pattern in the amount charged for each hour of rock climbing. $\newline$ For $1$ hour, the cost is $\$13$ . $\newline$ For $2$ hours, the cost is $\$21$ . $\newline$ For $3$ hours, the cost is $\$29$ . $\newline$ For $4$ hours, the cost is $\$37$ . $\newline$ We notice that each hour adds $\$8$ to the cost because $21 - 13 = 8$ , $29 - 21 = 8$ , and $37 - 29 = 8$ .
Determine Starting Amount: Determine the starting amount when $x = 0$ . If we subtract $\$8$ from the cost for $1$ hour, we get $\$5$ . This suggests that the base cost when $x = 0$ might be $\$5$ .
Formulate Rule: Formulate the rule based on the pattern and the starting amount. $\newline$ The rule to find the amount charged for $x$ hours is the starting amount plus $\$8$ times the number of hours. $\newline$ So, the rule is: Amount( $\$$ ) = $5 + 8x$ .
Check Rule with Given Values: Check the rule with the given values in the table to ensure it is correct. $\newline$ For $x = 1$ , Amount = $5 + 8(1) =$ $\$13$ . $\newline$ For $x = 2$ , Amount = $5 + 8(2) =$ $\$21$ . $\newline$ For $x = 3$ , Amount = $5 + 8(3) =$ $\$29$ . $\newline$ For $x = 4$ , Amount = $5 + 8(1) =$ $0$ $5 + 8(1) =$ $1$ . $\newline$ The rule works for all the given values.
Find Next Two Terms: Use the rule to find the next two terms in the sequence for $x = 5$ and $x = 6$ . For $x = 5$ , Amount = $5 + 8(5) = (\$)45$ . For $x = 6$ , Amount = $5 + 8(6) = (\$)53$ .