Alright, let's go through the problem step by step.
1. Greatest number of binders Eula can buy:
Eula needs to buy binders that cost [tex]$4 each. She has $[/tex]20. To find the greatest number of binders she can buy, we divide her total money by the cost per binder:
[tex]\[
\text{Greatest number of binders} = \left\lfloor \frac{20}{4} \right\rfloor = 5
\][/tex]
So, the greatest number of binders Eula can buy is 5.
2. Greatest number of notebooks Eula can buy:
Similarly, notebooks cost [tex]$2 each. To find the greatest number of notebooks she can buy, we divide her total money by the cost per notebook:
\[
\text{Greatest number of notebooks} = \left\lfloor \frac{20}{2} \right\rfloor = 10
\]
Therefore, the greatest number of notebooks Eula can buy is 10.
3. If Eula buys 7 notebooks, what is the greatest number of binders she can buy?:
First, calculate how much money Eula will spend on 7 notebooks:
\[
\text{Cost of 7 notebooks} = 7 \times 2 = 14
\]
Next, subtract this amount from Eula's total money to find out how much money she has left:
\[
\text{Money left} = 20 - 14 = 6
\]
Now, use the remaining money to buy binders, each costing $[/tex]4:
[tex]\[
\text{Greatest number of binders with remaining money} = \left\lfloor \frac{6}{4} \right\rfloor = 1
\][/tex]
So, if Eula buys 7 notebooks, the greatest number of binders she can buy with the remaining money is 1.
Putting all the answers together:
- The greatest number of binders Eula can buy: 5
- The greatest number of notebooks Eula can buy: 10
- If Eula buys 7 notebooks, she can buy at most 1 binder with the remaining money.
