Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Students 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 $3$ small bottles and $4$ large bottles, for a total of $116$ ounces. The day before, she drank $4$ small bottles and $4$ large bottles, for a total of $132$ ounces. How much does each bottle hold? $\newline$ The small bottle holds _ ounces and the large one holds _ ounces.

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Solve a system of equations using elimination: word problems

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Students 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

3

small bottles and

4

large bottles, for a total of

116

ounces. The day before, she drank

4

small bottles and

4

large bottles, for a total of

132

ounces. How much does each bottle hold?

\newline

The small bottle holds _____ ounces and the large one holds _____ ounces.

Equations Setup: Let's denote the volume of the small bottle as $S$ ounces and the large bottle as $L$ ounces. We can write two equations based on the given information: $\newline$ $1$ . For yesterday: $3S + 4L = 116$ ounces $\newline$ $2$ . For the day before: $4S + 4L = 132$ ounces
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 $L$ are already the same, so we can subtract the first equation from the second to eliminate $L$ . $\newline$ $(4S + 4L) - (3S + 4L) = 132 - 116$
Solving for S: Perform the subtraction to find the value of S: $\newline$ $4S - 3S + 4L - 4L = 132 - 116$ $\newline$ $S = 132 - 116$ $\newline$ $S = 16$ $\newline$ So, the small bottle holds $16$ ounces.
Substitute $S$ into Equation: Now that we know the value of $S$ , we can substitute it back into one of the original equations to find the value of $L$ . Let's use the first equation: $\newline$ $3(16) + 4L = 116$ $\newline$ $48 + 4L = 116$
Solving for L: Subtract $48$ from both sides to solve for $L$ : $\newline$ $4L = 116 - 48$ $\newline$ $4L = 68$ $\newline$ $L = 68 \div 4$ $\newline$ $L = 17$ $\newline$ So, the large bottle holds $17$ ounces.