Let's break this problem down step-by-step to determine the correct inequality for the number of dimes Ashley needs.
1. Convert Quarters to Dollars:
Ashley has 7 quarters. Each quarter is worth [tex]$0.25. Therefore, the total value of her quarters is:
\[
7 \times 0.25 = 1.75 \text{ dollars}
\]
2. Determine Additional Money Needed:
Ashley needs at least $[/tex]3.00 for lunch. We need to find out how much more money, in addition to her [tex]$1.75, she needs:
\[
\text{Needed amount} = 3.00 \text{ dollars}
\]
3. Establish Value of Dimes:
Each dime is worth $[/tex]0.10. If she has [tex]\( d \)[/tex] dimes, then the total value of her dimes is:
[tex]\[
0.10d \text{ dollars}
\][/tex]
4. Set Up Inequality:
We need Ashley's total amount of money (from both quarters and dimes) to be at least [tex]$3.00. The inequality that represents this situation is:
\[
1.75 + 0.10d \geq 3.00
\]
Now we will review each choice given in the problem:
- \((1)\) \(1.75 + d \geq 3.00\) - This is incorrect because it does not account for the fact that dimes are worth $[/tex]0.10 each.
- [tex]\((3)\)[/tex] [tex]\(1.75 + d \leq 3.00\)[/tex] - This is also incorrect because it has the wrong inequality sign and units for dimes.
- [tex]\((2)\)[/tex] [tex]\(1.75 + 0.10d \geq 3.00\)[/tex] - This is correct because it correctly models the total value needed with the correct units and inequality sign.
- [tex]\((4)\)[/tex] [tex]\(1.75 + 0.10d \leq 3.00\)[/tex] - This is incorrect because it has the wrong inequality sign.
Therefore, the correct inequality to determine the number of dimes, [tex]\( d \)[/tex], Ashley needs in her purse to be able to pay for lunch is:
[tex]\[
\boxed{1.75 + 0.10d \geq 3.00}
\][/tex]
So, the answer is:
[tex]\((2)\)[/tex] [tex]\(1.75 + 0.10d \geq 3.00\)[/tex].
