Question

You have $10.00 to spend on a birthday gift. So you go to the dollar store where each item costs exactly $1.25. You also have to pay $1.25 no matter how many items that you purchase. Let the number of items be represented by the variable n. How many items can you buy for the $10.00?

a.
8

b.
7

c.
6

d.
5

Answer 1

To find out how many items you can buy for a birthday gift, we need to set up the equation based on the total amount you have, which is $10.00.

The cost of each item is $1.25, and there is an additional cost of $1.25 for the purchase, regardless of how many items you buy. Thus, the total cost can be expressed as:

\[
\text{Total Cost} = 1.25 \cdot n + 1.25
\]

We also know that your total spending cannot exceed $10.00. Hence, we can set up the inequality:

\[
1.25n + 1.25 \leq 10
\]

To isolate \(n\), first subtract \(1.25\) from both sides:

\[
1.25n \leq 10 - 1.25
\]
\[
1.25n \leq 8.75
\]

Next, divide both sides by \(1.25\):

\[
n \leq \frac{8.75}{1.25}
\]
\[
n \leq 7
\]

Since \(n\) represents the number of items, it must be a whole number. The maximum value for \(n\) that satisfies the inequality is \(n = 7\).

So, the maximum number of items you can buy is:

**b. 7**