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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold 2525 packages of coffee and 3939 packages of tea, for which customers paid a total of $587\$587. The day before, 1010 packages of coffee and 3939 packages of tea was sold, which brought in a total of $422\$422. How much does each package cost?\newlinePer package, coffee costs $____\$\_\_\_\_ and tea 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 coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold 2525 packages of coffee and 3939 packages of tea, for which customers paid a total of $587\$587. The day before, 1010 packages of coffee and 3939 packages of tea was sold, which brought in a total of $422\$422. How much does each package cost?\newlinePer package, coffee costs $____\$\_\_\_\_ and tea costs $____\$\_\_\_\_.
  1. Equation 11: Let's denote the price of each package of coffee as cc and the price of each package of tea as tt. From the first day's sales, we have the equation 25c+39t=58725c + 39t = 587. This represents the total amount earned from selling 2525 packages of coffee and 3939 packages of tea.
  2. Equation 22: From the sales of the day before, we have the equation 10c+39t=42210c + 39t = 422. This represents the total amount earned from selling 1010 packages of coffee and 3939 packages of tea.
  3. Elimination Method: We now have a system of two equations:\newline11. 25c+39t=58725c + 39t = 587\newline22. 10c+39t=42210c + 39t = 422\newlineWe will use elimination to solve this system. To eliminate tt, we can subtract the second equation from the first equation.
  4. Subtraction Result: Subtracting the second equation from the first, we get:\newline(25c+39t)−(10c+39t)=587−422(25c + 39t) - (10c + 39t) = 587 - 422\newlineThis simplifies to:\newline15c=16515c = 165
  5. Coffee Price Calculation: Dividing both sides of the equation 15c=16515c = 165 by 1515, we find the price of each package of coffee:\newlinec=16515c = \frac{165}{15}\newlinec=11c = 11
  6. Tea Price Calculation: Now that we know c=11c = 11, we can substitute this value into one of the original equations to find tt. We'll use the second equation:\newline10c+39t=42210c + 39t = 422\newlineSubstituting cc with 1111 gives us:\newline10(11)+39t=42210(11) + 39t = 422
  7. Tea Price Calculation: Now that we know c=11c = 11, we can substitute this value into one of the original equations to find tt. We'll use the second equation:\newline10c+39t=42210c + 39t = 422\newlineSubstituting cc with 1111 gives us:\newline10(11)+39t=42210(11) + 39t = 422 Solving for tt, we get:\newline110+39t=422110 + 39t = 422\newlineSubtracting 110110 from both sides gives us:\newline39t=422−11039t = 422 - 110\newlinett00
  8. Tea Price Calculation: Now that we know c=11c = 11, we can substitute this value into one of the original equations to find tt. We'll use the second equation:\newline10c+39t=42210c + 39t = 422\newlineSubstituting cc with 1111 gives us:\newline10(11)+39t=42210(11) + 39t = 422 Solving for tt, we get:\newline110+39t=422110 + 39t = 422\newlineSubtracting 110110 from both sides gives us:\newline39t=422−11039t = 422 - 110\newlinett00 Dividing both sides of the equation tt00 by tt22, we find the price of each package of tea:\newlinett33\newlinett44

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