julia is offered a job selling advertising for two different companies. company a offers a base salary of…

julia is offered a job selling advertising for two different companies. company a offers a base salary of $30,000 per year plus a year - end bonus equal to 3% of her total sales. company b offers a base salary of $25,000 per year plus a year - end bonus equal to 5% of her total sales. which statement best describes the two offers?\no company a pays better when total sales are less than $37,500, but company b pays better when total sales exceed $37,500.\no company a pays better when total sales are less than $250,000, but company b pays better when total sales exceed $250,000.\no company b pays better when total sales are less than $37,500, but company a pays better when total sales exceed $37,500.\no company b pays better when total sales are less than $250,000, but company a pays better when total sales exceed $250,000.

julia is offered a job selling advertising for two different companies. company a offers a base salary of $30,000 per year plus a year - end bonus equal to 3% of her total sales. company b offers a base salary of $25,000 per year plus a year - end bonus equal to 5% of her total sales. which statement best describes the two offers?\no company a pays better when total sales are less than $37,500, but company b pays better when total sales exceed $37,500.\no company a pays better when total sales are less than $250,000, but company b pays better when total sales exceed $250,000.\no company b pays better when total sales are less than $37,500, but company a pays better when total sales exceed $37,500.\no company b pays better when total sales are less than $250,000, but company a pays better when total sales exceed $250,000.

Answer

Explanation:

Step1: Define the pay - equations

Let $x$ be the total sales. The pay from Company A, $P_A = 30000+0.03x$. The pay from Company B, $P_B=25000 + 0.05x$.

Step2: Find the break - even point

Set $P_A = P_B$. So, $30000+0.03x=25000 + 0.05x$. Subtract $0.03x$ from both sides: $30000=25000 + 0.05x-0.03x$. Simplify: $30000=25000+0.02x$. Subtract 25000 from both sides: $30000 - 25000=0.02x$. $5000 = 0.02x$. Solve for $x$: $x=\frac{5000}{0.02}=250000$.

Step3: Analyze the pay for different sales amounts

If $x < 250000$, let's take $x = 0$. $P_A=30000$ and $P_B = 25000$, so $P_A>P_B$. If $x>250000$, let's take $x = 300000$. $P_A=30000+0.03\times300000=30000 + 9000=39000$. $P_B=25000+0.05\times300000=25000 + 15000=40000$, so $P_B>P_A$.

Answer:

Company A pays better when total sales are less than $250,000, but company B pays better when total sales exceed $250,000.