Question

For a brunch party, Brett buys several cases of orange juice and cranberry juice. A case of orange juice (x) costs $15 and a case of cranberry juice (y) costs $8. Brett bought a total of 17 cases of juice and paid a total of $192. How many cases of orange juice did he buy?

Answer 1

Let's use a system of equations to solve the problem:

x = number of cases of orange juice

y = number of cases of cranberry juice

From the problem, we know that:

x + y = 17 (Brett bought a total of 17 cases of juice)

15x + 8y = 192 (Brett paid a total of $192 for the juice)

We can solve for one of the variables in the first equation and substitute it into the second equation:

x + y = 17

x = 17 - y

15x + 8y = 192

15(17 - y) + 8y = 192

255 - 15y + 8y = 192

-7y = -63

y = 9

So Brett bought 9 cases of cranberry juice. We can substitute this value back into the first equation to find how many cases of orange juice he bought:

x + y = 17

x + 9 = 17

x = 8

Therefore, Brett bought 8 cases of orange juice.