Danae is choosing between two jobs. One job pays an annual bonus of $[tex]$1,500[/tex] plus $[tex]$120[/tex] per day worked. The second job pays an annual bonus of $[tex]$2,500[/tex] plus $[tex]$110[/tex] per day worked. Which equation can be solved to determine after how many days, [tex]$d$[/tex], Danae would make the same amount of money regardless of the job she chooses?

A. [tex]$120 d+110 d=1,500+2,500$[/tex]
B. [tex]$120+110=1,500 d+2500 d$[/tex]
C. [tex]$120 d+1,500=110 d+2,500$[/tex]
D. [tex]$120 d+2,500=110 d+1,500$[/tex]

Question

Danae is choosing between two jobs. One job pays an annual bonus of $[tex]$1,500[/tex] plus $[tex]$120[/tex] per day worked. The second job pays an annual bonus of $[tex]$2,500[/tex] plus $[tex]$110[/tex] per day worked. Which equation can be solved to determine after how many days, [tex]$d$[/tex], Danae would make the same amount of money regardless of the job she chooses? 
 
A. [tex]$120 d+110 d=1,500+2,500$[/tex] 
B. [tex]$120+110=1,500 d+2500 d$[/tex] 
C. [tex]$120 d+1,500=110 d+2,500$[/tex] 
D. [tex]$120 d+2,500=110 d+1,500$[/tex]

GinnyAnswer · Answer

Define the total earnings for Job 1 as 120 d + 1500 . 
 Define the total earnings for Job 2 as 110 d + 2500 . 
 Set the total earnings equal to each other: 120 d + 1500 = 110 d + 2500 . 
 The equation to solve for the number of days is 120 d + 1 , 500 = 110 d + 2 , 500 ​ . 
 
 Explanation 
 
 Problem Analysis Let's analyze the problem. We are given two job options with different bonus amounts and daily rates. We need to find the equation that represents the scenario where the total earnings from both jobs are equal after working a certain number of days, denoted by 'd'. 
 
 Expressing Total Earnings Let's define the total earnings for each job as a function of the number of days worked, 'd'.

For Job 1, the total earnings are the bonus plus the daily rate times the number of days worked. This can be expressed as: 120 d + 1500 
 For Job 2, the total earnings are the bonus plus the daily rate times the number of days worked. This can be expressed as: 110 d + 2500 
 To find the number of days when the total earnings are the same for both jobs, we set the two expressions equal to each other: 120 d + 1500 = 110 d + 2500 
 
 Finding the Correct Equation Now, let's compare the equation we derived with the given options: 
 
 120 d + 110 d = 1 , 500 + 2 , 500 120 + 110 = 1 , 500 d + 2500 d 120 d + 1 , 500 = 110 d + 2 , 500 120 d + 2 , 500 = 110 d + 1 , 500 
 The equation that matches our derived equation is: 120 d + 1 , 500 = 110 d + 2 , 500 
 
 Final Answer Therefore, the equation that can be solved to determine after how many days, d, Danae would make the same amount of money regardless of the job she chooses is: 120 d + 1 , 500 = 110 d + 2 , 500 
 
 Examples 
 Imagine you're a freelance graphic designer choosing between two contracts. Contract A offers a base payment of $500 plus $50 per design, while Contract B offers a base payment of $200 plus $60 per design. By setting up an equation similar to the one in the problem, you can determine how many designs you need to complete for both contracts to pay the same amount. This helps you make an informed decision based on your expected workload and earning potential. Understanding such equations is crucial for making smart financial decisions in various real-life scenarios, from choosing job offers to comparing service plans.

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