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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA boy scout troop is selling Christmas trees at a local tree lot. In the morning, they sold 1717 Douglas Fir trees and 1212 Noble Fir trees, earning a total of $1,088\$1,088. In the afternoon, they sold 99 Douglas Fir trees and 1212 Noble Fir trees, earning a total of $864\$864. How much does each type of tree cost?\newlineA Douglas Fir costs $____\$\_\_\_\_ and a Noble Fir costs $____\$\_\_\_\_.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA boy scout troop is selling Christmas trees at a local tree lot. In the morning, they sold 1717 Douglas Fir trees and 1212 Noble Fir trees, earning a total of $1,088\$1,088. In the afternoon, they sold 99 Douglas Fir trees and 1212 Noble Fir trees, earning a total of $864\$864. How much does each type of tree cost?\newlineA Douglas Fir costs $____\$\_\_\_\_ and a Noble Fir costs $____\$\_\_\_\_.
  1. Define variables: Let's define two variables: let xx be the cost of one Douglas Fir tree and yy be the cost of one Noble Fir tree. We can write two equations based on the information given:\newlineFor the morning sales: 17x+12y=108817x + 12y = 1088\newlineFor the afternoon sales: 9x+12y=8649x + 12y = 864
  2. Elimination method: To solve this system using elimination, we want to eliminate one of the variables. We can do this by subtracting the second equation from the first equation:\newline(17x+12y)−(9x+12y)=1088−864(17x + 12y) - (9x + 12y) = 1088 - 864\newlineThis simplifies to:\newline17x−9x+12y−12y=1088−86417x - 9x + 12y - 12y = 1088 - 864
  3. Simplify equation: Now, we simplify the equation: 8x=2248x = 224
  4. Solve for x: Next, we solve for x by dividing both sides of the equation by 88: \newlinex=2248x = \frac{224}{8}\newlinex=28x = 28\newlineSo, a Douglas Fir tree costs $28\$28.
  5. Substitute xx back: Now that we have the value for xx, we can substitute it back into one of the original equations to solve for yy. We'll use the second equation:\newline9x+12y=8649x + 12y = 864\newline9(28)+12y=8649(28) + 12y = 864\newline252+12y=864252 + 12y = 864
  6. Solve for y: Subtract 252252 from both sides to solve for y:\newline12y=864−25212y = 864 - 252\newline12y=61212y = 612
  7. Solve for y: Subtract 252252 from both sides to solve for y:\newline12y=864−25212y = 864 - 252\newline12y=61212y = 612 Finally, divide both sides by 1212 to find the value of yy:\newliney=612/12y = 612 / 12\newliney=51y = 51\newlineSo, a Noble Fir tree costs $51\$51.

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