Question

Taylor has at most $125 to spend on basketballs and a new basketball jersey the brand of jersey that she wants to buy cost $45 she wants to buy one jersey and spend the rest on basketballs each basketball cost $12 which inequality shows the maximum number of basketballs that Taylor can buy

Answer 1

Let's denote the number of basketballs Taylor can buy as \( b \).

Taylor's total budget is $125. She wants to buy one basketball jersey that costs $45. This means the amount of money she has left after buying the jersey is:

\[
125 - 45 = 80
\]

The cost of each basketball is $12. Therefore, the total cost for \( b \) basketballs will be \( 12b \).

To find the maximum number of basketballs Taylor can buy without exceeding her budget of $80, we can set up the following inequality:

\[
12b \leq 80
\]

This represents the condition that the total cost of the basketballs must be less than or equal to the remaining budget after buying the jersey.

To solve for \( b \), we divide both sides of the inequality by 12:

\[
b \leq \frac{80}{12}
\]

This simplifies to:

\[
b \leq \frac{20}{3} \approx 6.67
\]

Since Taylor can only buy a whole number of basketballs, we take the largest whole number less than or equal to 6.67, which is 6.

Thus, the inequality that shows the maximum number of basketballs \( b \) that Taylor can buy is:

\[
12b \leq 80
\]