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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineNora wanted to stock up on drinks for an upcoming party. First, she spent $60\$60 on 1515 cases of juice and 1515 cases of soda, which is all the store had in stock. A few days later, she returned to the store and purchased an additional 55 cases of juice and 99 cases of soda, spending a total of $28\$28. What is the price of each drink?\newlineThe price for a case of juice is $\$____, and the price for a case of soda is $\$____

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineNora wanted to stock up on drinks for an upcoming party. First, she spent $60\$60 on 1515 cases of juice and 1515 cases of soda, which is all the store had in stock. A few days later, she returned to the store and purchased an additional 55 cases of juice and 99 cases of soda, spending a total of $28\$28. What is the price of each drink?\newlineThe price for a case of juice is $\$____, and the price for a case of soda is $\$____
  1. Equation 11: Let's denote the price of each case of juice as jj and the price of each case of soda as ss. Nora spent $60\$60 on 1515 cases of juice and 1515 cases of soda. This gives us the equation 15j+15s=6015j + 15s = 60.
  2. Equation 22: On her second trip, Nora purchased 55 cases of juice and 99 cases of soda for a total of $28\$28. This gives us the equation 5j+9s=285j + 9s = 28.
  3. Eliminate Variable: We now have a system of two equations. We need to eliminate one of the variables, jj or ss. To do this, we can multiply the second equation by 33 to match the coefficient of jj in the first equation. This gives us 15j+27s=8415j + 27s = 84.
  4. Substitute and Solve: We now subtract the first equation from the new third equation to eliminate jj. This gives us 12s=2412s = 24, or s=2s = 2.
  5. Final Solution: We substitute s=2s = 2 into the first equation and solve for jj. This gives us 15j+15(2)=6015j + 15(2) = 60, which simplifies to 15j+30=6015j + 30 = 60. Subtracting 3030 from both sides gives us 15j=3015j = 30, or j=2j = 2.

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