Lisa has $7.80 to spend on some tomatoes and a loaf of bread. Tomatoes cost $1.20 per pound, and a loaf of bread costs $1.80.
The inequality [tex]$1.20 x+1.80 \leq 7.80$[/tex] models this situation, where [tex]$x$[/tex] is the number of pounds of tomatoes.
Solve the inequality. How many pounds of tomatoes can Lisa buy?
A. [tex]$x \leq 8$[/tex]; Lisa can buy 8 pounds or less of tomatoes.
B. [tex]$x \geq 8$[/tex]; Lisa can buy 8 pounds or more of tomatoes.
C. [tex]$x \geq 5$[/tex]; Lisa can buy 5 pounds or more of tomatoes.
D. [tex]$x \leq 5$[/tex]; Lisa can buy 5 pounds or less of tomatoes.
Answer (2)
Subtract 1.80 from both sides of the inequality: 1.20 x ≤ 7.80 − 1.80 .
Simplify the right side: 1.20 x ≤ 6.00 .
Divide both sides by 1.20 : x ≤ 1.20 6.00 .
Simplify to find the maximum pounds of tomatoes: x ≤ 5 . The answer is x ≤ 5 .
Explanation
Understanding the Problem Lisa has $7.80 to spend, and she needs to buy a loaf of bread that costs $1.80 . She also wants to buy some tomatoes that cost $1.20 per pound. The inequality 1.20 x + 1.80 ≤ 7.80 represents this situation, where x is the number of pounds of tomatoes she can buy. Our goal is to solve this inequality to find the maximum number of pounds of tomatoes Lisa can buy.
Isolating the x term First, we need to isolate the term with x in the inequality. To do this, we subtract 1.80 from both sides of the inequality:
1.20 x + 1.80 − 1.80 ≤ 7.80 − 1.80
Simplifying the Inequality Now, we simplify both sides of the inequality:
1.20 x ≤ 6.00
Solving for x Next, we need to solve for x by dividing both sides of the inequality by 1.20 :
1.20 1.20 x ≤ 1.20 6.00
Finding the Maximum Pounds of Tomatoes Now, we simplify both sides of the inequality to find the value of x :
x ≤ 5
Final Answer The solution to the inequality is x ≤ 5 . This means Lisa can buy 5 pounds or less of tomatoes. Therefore, the correct answer is D.
Examples
Imagine you're planning a small party and have a budget for snacks. You know the cost of one essential item (like a cake) and the price per unit of another item (like juice boxes). Solving an inequality helps you determine the maximum number of juice boxes you can buy without exceeding your budget. This kind of problem-solving is useful in everyday budgeting and financial planning, ensuring you stay within your spending limits while getting the most out of your money.
By solving the inequality 1.20 x + 1.80 ≤ 7.80 , we find that x ≤ 5 . This means Lisa can buy 5 pounds or less of tomatoes. Thus, the correct answer is D: x ≤ 5 .
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