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. Maria has two reusable water bottles: a small one and a large one. Yesterday, she drank $4$ small bottles and $3$ large bottles, for a total of $3,030$ grams. The day before, she drank $2$ small bottles and $3$ large bottles, for a total of $2,262$ grams. How much does each bottle hold? $\newline$ The small bottle holds $\_$ grams and the large one holds $\_$ grams.

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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. Maria has two reusable water bottles: a small one and a large one. Yesterday, she drank

4

small bottles and

3

large bottles, for a total of

3,030

grams. The day before, she drank

2

small bottles and

3

large bottles, for a total of

2,262

grams. How much does each bottle hold?

\newline

The small bottle holds

\_

grams and the large one holds

\_

grams.

Set up equations: Let's denote the small bottle's capacity as $S$ grams and the large bottle's capacity as $L$ grams. We can set up two equations based on the given information: $\newline$ For the first day: $4S + 3L = 3,030$ grams $\newline$ For the second day: $2S + 3L = 2,262$ grams
Elimination method: To solve using elimination, we need to eliminate one of the variables. We can do this by multiplying the second equation by $2$ , so that the coefficient of $S$ in both equations is the same: $\newline$ First equation: $4S + 3L = 3,030$ $\newline$ Second equation (multiplied by $2$ ): $4S + 6L = 4,524$
Subtract and solve: Now, we subtract the second equation from the first equation to eliminate $S$ : $(4S + 3L) - (4S + 6L) = 3,030 - 4,524$ This simplifies to: $-3L = -1,494$
Solve for L: We divide both sides by $-3$ to solve for $L$ : $L = \frac{-1,494}{-3}$ $L = 498$ So, the large bottle holds $498$ grams.
Substitute and solve: Now that we have the value for $L$ , we can substitute it back into one of the original equations to solve for $S$ . We'll use the second equation: $\newline$ $2S + 3(498) = 2,262$ $\newline$ $2S + 1,494 = 2,262$ $\newline$ $2S = 2,262 - 1,494$ $\newline$ $2S = 768$
Final solution: Finally, we divide both sides by $2$ to solve for $S$ : $S = \frac{768}{2}$ $S = 384$ So, the small bottle holds $384$ grams.