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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineFernando just got his commercial driver's license and is starting a new career as a truck driver. Getting trained and licensed involved a one-time cost of $437\$437. Gas and insurance end up costing him $2\$2 per kilometer. For his first delivery, Fernando will get paid $403\$403 plus $3\$3 per kilometer that he drives. If he drives a certain distance on this delivery, Fernando will break even, making back all the money he had to spend. How much would both the costs and the earnings be? What distance would he have to drive?\newlineThe costs and the earnings would both be $____\$\_\_\_\_ if Fernando drives ____\_\_\_\_ kilometers.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineFernando just got his commercial driver's license and is starting a new career as a truck driver. Getting trained and licensed involved a one-time cost of $437\$437. Gas and insurance end up costing him $2\$2 per kilometer. For his first delivery, Fernando will get paid $403\$403 plus $3\$3 per kilometer that he drives. If he drives a certain distance on this delivery, Fernando will break even, making back all the money he had to spend. How much would both the costs and the earnings be? What distance would he have to drive?\newlineThe costs and the earnings would both be $____\$\_\_\_\_ if Fernando drives ____\_\_\_\_ kilometers.
  1. Define variables: Let's define the variables:\newlineLet xx be the distance Fernando drives in kilometers.\newlineLet CC be the total cost for Fernando.\newlineLet EE be the total earnings for Fernando.
  2. Total cost equation: We can write the equation for the total cost CC that Fernando incurs: C=437+2xC = 437 + 2x (since the one-time cost is $437\$437 and the cost per kilometer is $2\$2).
  3. Total earnings equation: We can write the equation for the total earnings EE that Fernando makes: E=403+3xE = 403 + 3x (since the base pay is $403\$403 and the pay per kilometer is $3\$3).
  4. Find break-even point: To find the break-even point, we set the total costs equal to the total earnings:\newlineC=EC = E\newline437+2x=403+3x437 + 2x = 403 + 3x
  5. Solve for x: Now, we solve for x using substitution or rearranging the equation:\newline437−403=3x−2x437 - 403 = 3x - 2x\newline34=x34 = x
  6. Substitute xx back: We substitute xx back into either the cost or the earnings equation to find the total amount:\newlineC=437+2(34)C = 437 + 2(34)\newlineC=437+68C = 437 + 68\newlineC=505C = 505
  7. Check earnings: We check the earnings with the distance found to ensure it matches the costs:\newlineE=403+3(34)E = 403 + 3(34)\newlineE=403+102E = 403 + 102\newlineE=505E = 505

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