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.

Question

• 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.

Answer 1

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