Question

tatiana reads 40 pages of her book every night for x number of nights. write an expression that represents the number of pages she has read.
jonathan ran 5 days this week. the most he ran in one day was 3.5 miles. write an inequality that shows the distance jonathan could have run any day this week?
every day luis buys 5 more baseball cards to add to his collection. if he already had 25 baseball cards before making any purchases, how many will he have on day 20?

Explanation:

First Sub - Question (Tatiana's Reading)

Step1: Identify the relationship

Tatiana reads 40 pages per night, and she reads for x nights. The total number of pages read is the number of pages per night multiplied by the number of nights.

Step2: Write the expression

If we let \( P \) be the total number of pages read, then the expression is \( P = 40\times x\), which can be written as \( 40x \).

Step1: Define the variable

Let \( d \) be the distance (in miles) Jonathan ran on a particular day.

Step2: Set up the inequality

We know that the most he ran in one day was 3.5 miles. This means that the distance he ran on any day, \( d \), must be less than or equal to 3.5 miles. So the inequality is \( d\leq3.5 \).

Step1: Identify the pattern

Luis starts with 25 cards and buys 5 cards each day. This is an arithmetic sequence problem where the initial term \( a_1 = 25\) and the common difference \( d = 5\). The formula for the \( n\)th term of an arithmetic sequence is \( a_n=a_1+(n - 1)d\). Here, we want to find the number of cards on day 20, so \( n = 20\).

Step2: Substitute the values into the formula

First, substitute \( a_1 = 25\), \( d = 5\), and \( n = 20\) into the formula:
\(a_{20}=25+(20 - 1)\times5\)

Step3: Simplify the expression

First, calculate \( 20 - 1=19\). Then, \( 19\times5 = 95\). Then, \( 25+95=120\).

Answer:

The expression is \( 40x \).

Second Sub - Question (Jonathan's Running)