Sachi and Olivia are coaches on the soccer team. They bring bottles of water and lemonade to a game. Each bottle of water contains the same amount of water, and each bottle of lemonade contains the same amount of lemonade.
• Sachi brings 22 bottles of water and 15 bottles of lemonade, which is a total of 564 fluid ounces.
• Olivia brings 28 bottles of water and 10 bottles of lemonade, which is a total of 536 fluid ounces.
Sachi and Olivia bring enough water and lemonade so that each player gets 2 bottles of water and 1 bottle of lemonade.
How many total fluid ounces does each player get? Enter the answer in the box.
To find out how many total fluid ounces each player gets, we need to calculate the total number of fluid ounces brought by Sachi and Olivia and then divide it by the total number of players.
First, let's calculate the total number of fluid ounces brought by Sachi:
- Sachi brings 22 bottles of water, and each bottle contains the same amount of water, so the total amount of water brought by Sachi is 22 * (amount of water in one bottle).
- Sachi also brings 15 bottles of lemonade, and each bottle contains the same amount of lemonade, so the total amount of lemonade brought by Sachi is 15 * (amount of lemonade in one bottle).
- Adding these two amounts together will give us the total fluid ounces brought by Sachi.
Next, let's calculate the total number of fluid ounces brought by Olivia:
- Olivia brings 28 bottles of water, and each bottle contains the same amount of water, so the total amount of water brought by Olivia is 28 * (amount of water in one bottle).
- Olivia also brings 10 bottles of lemonade, and each bottle contains the same amount of lemonade, so the total amount of lemonade brought by Olivia is 10 * (amount of lemonade in one bottle).
- Adding these two amounts together will give us the total fluid ounces brought by Olivia.
Now, if each player gets 2 bottles of water and 1 bottle of lemonade, we need to divide the total fluid ounces by the number of players to find out how many fluid ounces each player gets.
Let's calculate it step by step:
1. To find the amount of water in one bottle, divide the total amount of water brought by Sachi (22 bottles) by the total number of fluid ounces (564 fluid ounces).
amount of water in one bottle = (total amount of water brought by Sachi) / (total number of water bottles brought by Sachi)
2. To find the amount of lemonade in one bottle, divide the total amount of lemonade brought by Sachi (15 bottles) by the total number of fluid ounces (564 fluid ounces).
amount of lemonade in one bottle = (total amount of lemonade brought by Sachi) / (total number of lemonade bottles brought by Sachi)
3. Repeat steps 1 and 2 for Olivia to find the amount of water and lemonade in one bottle brought by Olivia.
4. Calculate the total fluid ounces brought by Sachi and Olivia by adding the total fluid ounces brought by each individually.
5. Divide the total fluid ounces by the number of players (2 bottles of water and 1 bottle of lemonade per player) to find out how many total fluid ounces each player gets.
Once you find the total fluid ounces each player gets, enter your answer in the box provided.
Let's set up a system of equations to solve this problem.
Let's represent the amount of fluid ounces in a bottle of water as "w" and the amount of fluid ounces in a bottle of lemonade as "l".
From the first piece of information, we know that:
22w + 15l = 564 --------------(1)
From the second piece of information, we know that:
28w + 10l = 536 --------------(2)
Now let's solve this system of equations. We can multiply equation (2) by 3 to make the coefficient of "l" the same in both equations.
3(28w + 10l) = 3(536)
84w + 30l = 1608
Now we can subtract equation (1) from this new equation:
(84w + 30l) - (22w + 15l) = 1608 - 564
62w + 15l = 1044 --------------(3)
We can multiply equation (1) by 15 and equation (3) by 22 to make the coefficient of "l" the same in both equations.
15(22w + 15l) = 15(564)
330w + 225l = 8460
22(62w + 15l) = 22(1044)
1364w + 330l = 22968
Now we can subtract equation (3) from this new equation:
(1364w + 330l) - (330w + 15l) = 22968 - 8460
1034w + 315l = 14508
Now we have a system of two linear equations:
62w + 15l = 1044 --------------(3)
1034w + 315l = 14508
Let's multiply equation (3) by 1034 and equation (1) by 62 to make the coefficients of "w" the same in both equations.
1034(62w + 15l) = 1034(1044)
62708w + 15410l = 1080256
62(62w + 15l) = 62(1044)
3844w + 930l = 34968
Now we can subtract equation (3) from equation (1):
(62708w + 15410l) - (3844w + 930l) = 1080256 - 34968
58864w + 14480l = 1045288
Now we have a system of two linear equations:
58864w + 14480l = 1045288
1034w + 315l = 14508
Let's solve this system using elimination. Multiply equation (2) by -3:
-3(1034w + 315l) = -3(14508)
-3102w - 945l = -43524
Now subtract equation (4) from equation (1):
(58864w + 14480l) - (-3102w - 945l) = 1045288 - (-43524)
61966w + 15425l = 1088812
Now we have a system of two linear equations:
61966w + 15425l = 1088812
-3102w - 945l = -43524
Adding equation (2) and equation (5), we get:
(61966w + 15425l) + (-3102w - 945l) = 1088812 + (-43524)
58864w + 14480l - 3102w - 945l = 1045288 - 43524
55762w + 13535l = 1001764
Now we have a system of two linear equations:
55762w + 13535l = 1001764
-3102w - 945l = -43524
Let's multiply equation (6) by 9 and equation (5) by -3102 to make the coefficients of "w" the same in both equations.
9(55762w + 13535l) = 9(1001764)
501858w + 121815l = 9015876
-3102(-3102w - 945l) = -3102(-43524)
9624404w + 2934090l = 135101248
Now we can subtract equation (6) from equation (7):
(9624404w + 2934090l) - (501858w + 121815l) = 135101248 - 9015876
9122546w + 2812275l = 126085372
Let's find the total fluid ounces brought by Sachi and Olivia.
Sachi brings 22 bottles of water and each bottle contains the same amount of water. So, the total fluid ounces of water brought by Sachi is 22 * X, where X is the amount of water in each bottle.
Sachi also brings 15 bottles of lemonade and each bottle contains the same amount of lemonade. So, the total fluid ounces of lemonade brought by Sachi is 15 * Y, where Y is the amount of lemonade in each bottle.
Similarly, Olivia brings 28 bottles of water and each bottle contains the same amount of water. So, the total fluid ounces of water brought by Olivia is 28 * X.
Olivia also brings 10 bottles of lemonade and each bottle contains the same amount of lemonade. So, the total fluid ounces of lemonade brought by Olivia is 10 * Y.
According to the given information, the total fluid ounces brought by Sachi and Olivia is 564 + 536 = 1100.
So, we can write the equation: 22 * X + 15 * Y + 28 * X + 10 * Y = 1100.
Now, we need to find the values of X and Y.
We know that each player gets 2 bottles of water and 1 bottle of lemonade. So, the total fluid ounces received by each player is 2 * X + 1 * Y.
Since there are no additional bottles of water or lemonade, the total fluid ounces received by each player should be equal to the total fluid ounces brought by Sachi and Olivia, which is 1100.
So, we can write the equation: 2 * X + 1 * Y = 1100.
To solve these equations, we can use a system of linear equations solver.