Discover the best answers to your questions with the help of IDNLearn.com. Find the information you need quickly and easily with our comprehensive and accurate Q&A platform.
At a supermarket, oranges cost [tex] \$1.30 [/tex] per pound and pears cost [tex] \$1.90 [/tex] per pound. Misha spent less than [tex] \$10.00 [/tex] on 2 pounds of oranges and [tex] x [/tex] pounds of pears. Which inequality represents this situation?
A. [tex] 2(1.30) + 1.90x \ \textless \ 10.00 [/tex] B. [tex] 2(1.90) + 1.30x \ \textless \ 10.00 [/tex] C. [tex] (1.30 + 1.90)x \ \textless \ 10.00 [/tex] D. [tex] 2(1.30 + 1.90)x \ \textless \ 10.00 [/tex]
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]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.
