To determine which inequality represents Misha's spending at the supermarket, let's break down the situation step by step.
1. Given Cost Per Pound:
- The cost of oranges is [tex]$1.30 per pound.
- The cost of pears is $[/tex]1.90 per pound.
2. Misha's Shopping:
- Misha bought 2 pounds of oranges.
- Misha also bought [tex]\( x \)[/tex] pounds of pears.
- The total amount Misha spent is less than $10.00.
3. Calculating the Cost of Oranges:
- Misha bought 2 pounds of oranges, so the total cost of the oranges is:
[tex]\[
2 \text{ pounds} \times 1.30 \text{ dollars/pound} = 2.60 \text{ dollars}
\][/tex]
4. Setting Up the Inequality:
- Let [tex]\( x \)[/tex] be the number of pounds of pears.
- The cost of [tex]\( x \)[/tex] pounds of pears would be:
[tex]\[
1.90 \text{ dollars/pound} \times x = 1.90x \text{ dollars}
\][/tex]
- The total expenditure combining the cost of oranges and pears is:
[tex]\[
2.60 \text{ dollars} + 1.90x \text{ dollars} < 10.00 \text{ dollars}
\][/tex]
5. Identifying the Correct Inequality:
- We must choose from the following options:
[tex]\[
\left(\frac{1.30 + 1.90}{2}\right)x < 10.00
\][/tex]
[tex]\[
2(1.30)+1.90x < 10.00
\][/tex]
[tex]\[
2(1.90)+1.30x < 10.00
\][/tex]
[tex]\[
2(1.30 + 1.90)x < 10.00
\][/tex]
Our derived inequality for Misha's total spending was:
[tex]\[
2.60 + 1.90x < 10.00
\][/tex]
Comparing this to the given options, we find that the correct inequality is:
[tex]\[
2(1.30) + 1.90x < 10.00
\][/tex]
Therefore, the inequality that represents this situation is:
[tex]\[
2(1.30)+1.90 x<10.00
\][/tex]
