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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineFred, an office manager, needs to find a courier to deliver a package. The first courier he is considering charges a fee of $10\$10 plus $3\$3 per pound. The second charges $15\$15 plus $2\$2 per pound. Fred determines that, given his package's weight, the two courier services are equivalent in terms of cost. What is the weight? How much will it cost?\newlineAt a package weight of ‾\underline{\quad} pounds, the two couriers both cost $‾\$\underline{\quad}.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineFred, an office manager, needs to find a courier to deliver a package. The first courier he is considering charges a fee of $10\$10 plus $3\$3 per pound. The second charges $15\$15 plus $2\$2 per pound. Fred determines that, given his package's weight, the two courier services are equivalent in terms of cost. What is the weight? How much will it cost?\newlineAt a package weight of ‾\underline{\quad} pounds, the two couriers both cost $‾\$\underline{\quad}.
  1. Define Variables: Let's define the variables. Let xx represent the weight of the package in pounds, and let yy represent the total cost for the courier service.
  2. Write Equations: Write the equations based on the given information. For the first courier, the cost is $10\$10 plus $3\$3 per pound, which gives us the equation y=3x+10y = 3x + 10. For the second courier, the cost is $15\$15 plus $2\$2 per pound, which gives us the equation y=2x+15y = 2x + 15.
  3. Set Equations Equal: Since the costs are equivalent, we can set the two equations equal to each other to find the weight of the package. So, we have 3x+10=2x+153x + 10 = 2x + 15.
  4. Solve for x: Solve for x by subtracting 2x2x from both sides of the equation to isolate xx on one side. This gives us x=15−10x = 15 - 10.
  5. Calculate x: Calculate the value of x. x=15−10=5x = 15 - 10 = 5. So, the weight of the package is 55 pounds.
  6. Substitute xx: Substitute the value of xx back into either of the original equations to find the total cost yy. Using the first courier's equation: y=3(5)+10y = 3(5) + 10.
  7. Calculate Total Cost: Calculate the total cost yy. y=3(5)+10=15+10=25y = 3(5) + 10 = 15 + 10 = 25. So, the cost for both couriers is $25\$25.

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