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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineLowell City Cafe recently introduced a new flavor of coffee. They served 6767 grande cups and 3636 jumbo cups of the new coffee today, which equaled a total of 48,78148,781 grams. The day before, 6767 grande cups and 6464 jumbo cups were served, which used a total of 65,72165,721 grams. How much coffee is required to make each size?\newlineThere are _\_ grams in a grande cup of coffee and _\_ grams in a jumbo one.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineLowell City Cafe recently introduced a new flavor of coffee. They served 6767 grande cups and 3636 jumbo cups of the new coffee today, which equaled a total of 48,78148,781 grams. The day before, 6767 grande cups and 6464 jumbo cups were served, which used a total of 65,72165,721 grams. How much coffee is required to make each size?\newlineThere are _\_ grams in a grande cup of coffee and _\_ grams in a jumbo one.
  1. Define variables: Define variables for the grams of coffee per grande cup gg and per jumbo cup jj. We have two scenarios: 6767 grande cups and 3636 jumbo cups totaling 48,78148,781 grams, and 6767 grande cups and 6464 jumbo cups totaling 65,72165,721 grams. This leads to the equations:\newline11. 67g+36j=48,78167g + 36j = 48,781\newline22. 67g+64j=65,72167g + 64j = 65,721
  2. Eliminate variable: Eliminate variable gg by subtracting the first equation from the second:\newline(67g+64j)−(67g+36j)=65,721−48,781(67g + 64j) - (67g + 36j) = 65,721 - 48,781\newline28j=16,94028j = 16,940
  3. Solve for j: Solve for j:\newlinej=16,94028j = \frac{16,940}{28}\newlinej=605j = 605
  4. Substitute and solve: Substitute j=605j = 605 into the first equation to solve for gg:67g+36(605)=48,78167g + 36(605) = 48,78167g+21,780=48,78167g + 21,780 = 48,78167g=48,781−21,78067g = 48,781 - 21,78067g=27,00167g = 27,001
  5. Final solution: Solve for gg:g=27,00167g = \frac{27,001}{67}g=403g = 403

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