During one school year, Billy Bob earned $25 for each Math test he passed and was ined $50 for each Math test he failed. By the end of the school year, Billy Bob passes 7 times as many Math tests as he failed and he had a total of $375. How many tests did he pass?
Failed X tests.
Passed 7X tests.
25*7X - 50*X = 375,
175X - 50X = 375,
125X = 375,
X = 3 Tests failed.
7x = 7*3 = 21 Tests passed.
5X2-(-3)
the answer is 21 tests passed
To solve this problem, let's assign variables to the unknowns.
Let's say the number of Math tests Billy Bob passed is 'x'.
Then, the number of Math tests Billy Bob failed is 'y'.
According to the given information:
- Billy Bob earned $25 for each Math test he passed, so the total amount earned from passing tests is 25x.
- Billy Bob earned $50 for each Math test he failed, so the total amount earned from failing tests is 50y.
- Billy Bob passed 7 times as many Math tests as he failed, so we can write the equation: x = 7y.
- The total amount earned from all the tests is $375, so the equation becomes: 25x + 50y = 375.
Now, we can use these equations to solve for 'x', the number of tests passed.
Substituting the value of x from the first equation into the second equation: 25(7y) + 50y = 375.
Simplifying the equation: 175y + 50y = 375.
Combining like terms: 225y = 375.
Dividing both sides of the equation by 225: y = 375 / 225 = 5/3.
Since we cannot have a fraction of a test, we need to check if this value of 'y' is valid. We can substitute y = 5/3 back into the original equation x = 7y:
x = 7(5/3) = 35/3, which is still a fraction.
Therefore, there is no whole number solution that satisfies the given conditions.