Question

Sarah will spend 26$ on candy , each item cost 3$ and she has a coupon for 5$ discount .. what is this inequality

Answer 1

To find the inequality representing Sarah's situation, we need to consider the total cost of the candy.

Let \( x \) be the number of candy items Sarah buys. Each item costs \( 3 \) dollars, so the total cost for \( x \) items is \( 3x \) dollars.

With the \( 5 \) dollar discount from her coupon, Sarah's total expenditure can be expressed as:

\[
3x - 5
\]

We know that Sarah will spend up to \( 26 \) dollars on candy, so we set up the following inequality:

\[
3x - 5 \leq 26
\]

This inequality reflects that the cost of the candy after applying the coupon should not exceed \( 26 \) dollars.

To solve for \( x \), you can add \( 5 \) to both sides:

\[
3x \leq 31
\]

Then, divide by \( 3 \):

\[
x \leq \frac{31}{3}
\]

Thus, \( x \leq 10.33 \). Since \( x \) represents the number of candy items bought, it must be a whole number. Therefore, the maximum integer value for \( x \) is \( 10 \).

So, the final inequality is:

\[
3x - 5 \leq 26
\]

And \( x \) must be a whole number less than or equal to \( 10 \).