Questions: At a supermarket, oranges cost 1.30 per pound and pears cost 1.90 per pound. Misha spent less than 10.00 on 2 pounds of oranges and x pounds of pears. Which inequality represents this situation? (1.30+1.90)/2 x<10.00 2(1.30)+1.90 x<10.00 2(1.90)+1.30 x<10.00 2(1.30+1.90) x<10.00

At a supermarket, oranges cost 1.30 per pound and pears cost 1.90 per pound. Misha spent less than 10.00 on 2 pounds of oranges and x pounds of pears. Which inequality represents this situation?
(1.30+1.90)/2 x<10.00
2(1.30)+1.90 x<10.00
2(1.90)+1.30 x<10.00
2(1.30+1.90) x<10.00

Transcript text: Question At a supermarket, oranges cost $\$ 1.30$ per pound and pears cost $\$ 1.90$ per pound. Misha spent less than $\$ 10.00$ on 2 pounds of oranges and $x$ pounds of pears. Which inequality represents this situation? $\left(\frac{1.30+1.90}{2}\right) x<10.00$ $2(1.30)+1.90 x<10.00$ $2(1.90)+1.30 x<10.00$ $2(1.30+1.90) x<10.00$

Solution

Solution Steps

Step 1: Understand the Problem

Misha buys 2 pounds of oranges and $ x $ pounds of pears. The cost of oranges is \$1.30 per pound, and the cost of pears is \$1.90 per pound. Misha spends less than \$10.00 in total. We need to find the inequality that represents this situation.

Step 2: Calculate the Cost of Oranges

The cost of 2 pounds of oranges is: \[ 2 \times 1.30 = 2.60 \]

Step 3: Set Up the Inequality

The total cost of 2 pounds of oranges and $ x $ pounds of pears is: \[ 2.60 + 1.90x \]

Since Misha spent less than \$10.00, the inequality is: \[ 2.60 + 1.90x < 10.00 \]

Step 4: Match the Inequality with the Options

The inequality $ 2.60 + 1.90x < 10.00 $ matches the first option: \[ 2(1.30) + 1.90x < 10.00 \]