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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineStudents in a health class are tracking how much water they consume each day. Victoria has two reusable water bottles: a small one and a large one. Yesterday, she drank 33 small bottles and 44 large bottles, for a total of 116116 ounces. The day before, she drank 44 small bottles and 44 large bottles, for a total of 132132 ounces. How much does each bottle hold?\newlineThe small bottle holds _____ ounces and the large one holds _____ ounces.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineStudents in a health class are tracking how much water they consume each day. Victoria has two reusable water bottles: a small one and a large one. Yesterday, she drank 33 small bottles and 44 large bottles, for a total of 116116 ounces. The day before, she drank 44 small bottles and 44 large bottles, for a total of 132132 ounces. How much does each bottle hold?\newlineThe small bottle holds _____ ounces and the large one holds _____ ounces.
  1. Equations Setup: Let's denote the volume of the small bottle as SS ounces and the large bottle as LL ounces. We can write two equations based on the given information:\newline11. For yesterday: 3S+4L=1163S + 4L = 116 ounces\newline22. For the day before: 4S+4L=1324S + 4L = 132 ounces
  2. Elimination Method: To use elimination, we need to make the coefficients of one of the variables the same in both equations. We can see that the coefficients of LL are already the same, so we can subtract the first equation from the second to eliminate LL. \newline(4S+4L)−(3S+4L)=132−116(4S + 4L) - (3S + 4L) = 132 - 116
  3. Solving for S: Perform the subtraction to find the value of S:\newline4S−3S+4L−4L=132−1164S - 3S + 4L - 4L = 132 - 116\newlineS=132−116S = 132 - 116\newlineS=16S = 16\newlineSo, the small bottle holds 1616 ounces.
  4. Substitute SS into Equation: Now that we know the value of SS, we can substitute it back into one of the original equations to find the value of LL. Let's use the first equation:\newline3(16)+4L=1163(16) + 4L = 116\newline48+4L=11648 + 4L = 116
  5. Solving for L: Subtract 4848 from both sides to solve for LL: \newline4L=116−484L = 116 - 48\newline4L=684L = 68\newlineL=68÷4L = 68 \div 4\newlineL=17L = 17\newlineSo, the large bottle holds 1717 ounces.

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