Final answer:
The cost of a case of juice is $20 and the cost of a case of bottled water is $15. This was determined by setting up a system of linear equations based on the expenditures of the math club and science club and solving for the variables representing the cost of juice and water.
Step-by-step explanation:
To solve the problem of determining the cost of a case of juice and a case of bottled water from the details provided by the math club and the science club's spending, we can set up a system of linear equations.
Let's define x as the cost of one case of juice and y as the cost of one case of bottled water. From the math club's spending, we have the first equation:
6x + y = $135
From the science club's spending, we have the second equation:
4x + 2y = $110
To find the values of x and y, we can use either substitution or elimination method. Here's how you can solve it by elimination:
- Multiply the first equation by 2 so that the coefficients of y become equal. This gives us 12x + 2y = $270.
- Subtract the second equation from this new equation: (12x + 2y) - (4x + 2y) = $270 - $110.
- Simplify to find the value of x: 8x = $160 or x = $20.
- To find y, substitute x = $20 into any of the original equations. Let's use the first equation: 6(20) + y = $135.
- Simplify to solve for y: 120 + y = $135 or y = $15.
Therefore, the cost of a case of juice is $20 and the cost of a case of bottled water is $15.