Paul wants to go to a concert. The concert ticket costs $125. Paul earns $30 for each lawn he mows and $15 for each car he washes. Which inequality best represents the number of lawns he will have to mow and the number of cars he will have to wash in order to buy a concert ticket?

$30l + 15w \geq 125

Question

$30l + 15w \geq 125

GinnyAnswer · Answer

Define variables: Let l be the number of lawns and w be the number of cars. 
 Express total earnings: Paul earns 30 l + 15 w . 
 Set up the inequality: The total earnings must be greater than or equal to the ticket cost: 30 l + 15 w ≥ 125 . 
 The inequality representing the situation is: 30 l + 15 w ≥ 125 ​ . 
 
 Explanation 
 
 Formulating the Inequality Let l be the number of lawns Paul mows and w be the number of cars he washes. Paul earns $30 for each lawn he mows, so he earns 30 l dollars from mowing lawns. He earns $15 for each car he washes, so he earns 15 w dollars from washing cars. The total amount he earns is 30 l + 15 w . To buy the concert ticket, his total earnings must be greater than or equal to the cost of the ticket, which is $125 . Therefore, the inequality is 30 l + 15 w ≥ 125 . 
 
 Stating the Inequality The inequality that represents the number of lawns he will have to mow and the number of cars he will have to wash in order to buy a concert ticket is 30 l + 15 w ≥ 125 .

Examples 
 Imagine you're organizing a fundraising event to reach a specific financial goal. This problem is similar to figuring out how many items you need to sell at different prices to meet or exceed your target amount. For example, if you're selling cookies for $2 each and raffle tickets for $5 each, you can use an inequality to determine the number of cookies and raffle tickets you need to sell to reach your fundraising goal. Understanding how to set up and solve these inequalities helps in planning and achieving financial targets in various real-life scenarios.

Anonymous · Answer

The inequality that represents the earnings needed for Paul to buy a concert ticket is 30 l + 15 w ≥ 125 . This means he can mix the number of lawns mowed and cars washed to reach or exceed the ticket cost. Thus, he needs to find combinations of l and w that satisfy this inequality. 
 ;

Answer (2)

Related Questions in Mathematics

📝 Answered - Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-6)^2=44$[/tex] B. [tex]$(x-3)^2=17$[/tex] C. [tex]$(x-6)^2=20$[/tex] D. [tex]$(x-3)^2=14$[/tex]

📝 Answered - Which phrase best describes the translation from the graph [tex]y=6 x^2[/tex] to the graph of [tex]y=6(x+1)^2[/tex]? A. 6 units left B. 6 units right C. 1 unit left D. 1 unit right

📝 Answered - What expression is equivalent to [tex]$\left(5 z^2+3 z+2\right)^2$[/tex] ? A. [tex]$5 z^4+3 z^2+4$[/tex] B. [tex]$5 z^4+9 z^2+4$[/tex] C. [tex]$25 z^4+30 z^3+19 z^2+12 z+4$[/tex] D. [tex]$25 z^4+30 z^3+29 z^2+12 z+4$[/tex]

📝 Answered - The graph of [tex]y=\frac{5}{4} x+1[/tex] is shown below. The coordinate ([tex]0, y[/tex]) is a solution of the equation. Given the [tex]x[/tex]-value of 0, what is the value of the [tex]y[/tex]-coordinate for the coordinate ([tex]0, y[/tex])? [tex]y=[/tex] [blank]

📝 Answered - If [tex]f(-2)=0[/tex], what are all the factors of the function [tex]f(x)=x^3-2 x^2-68 x-120[/tex]? Use the Remainder Theorem. A. [tex](x+2)(x+60)[/tex] B. [tex](x-2)(x-60)[/tex] C. [tex](x-10)(x+2)(x+6)[/tex] D. [tex](x+10)(x-2)(x-6)[/tex]