Students in a health class are tracking how much water they consume each day. Brandon has two reusable water bottles: a small one and a large one. Yesterday, he drank 2 small bottles and 4 large bottles, for a total of 3,060 grams. The day before, he drank 2 small bottles and 2 large bottles, for a total of 1,962 grams. How much does each bottle hold?
To find out how much each water bottle holds, we can set up a system of equations based on the given information.
Let's assume that the small bottle holds X grams of water, and the large bottle holds Y grams of water.
From the information given, we know that Brandon drank 2 small bottles and 4 large bottles yesterday, totaling 3,060 grams. Using this, we can write the following equation:
2X + 4Y = 3,060 -- (Equation 1)
Similarly, the day before, Brandon drank 2 small bottles and 2 large bottles, totaling 1,962 grams. So, we can write another equation:
2X + 2Y = 1,962 -- (Equation 2)
Now, we have a system of equations that we can solve to find the values of X and Y.
We can begin by multiplying Equation 2 by 2 to make the coefficients of X in both equations equal:
4X + 4Y = 3,924 -- (Equation 3)
Now, we can subtract Equation 3 from Equation 1, which will eliminate the X variable:
(2X + 4Y) - (4X + 4Y) = 3,060 - 3,924
Simplifying this equation, we have:
-2X = -864
Dividing both sides by -2, we find:
X = 432
Now that we have the value of X, we can substitute it back into Equation 1 to solve for Y:
2(432) + 4Y = 3,060
864 + 4Y = 3,060
Subtracting 864 from both sides, we have:
4Y = 2,196
Dividing both sides by 4, we find:
Y = 549
Therefore, the small water bottle holds 432 grams, and the large water bottle holds 549 grams.