Almaz Has Taken2 Tests.Her Average Score Is 7 Out Of 10.The Product Of Her Score Is45. What Did She Score In Each Test?
To find out what Almaz scored in each test, let's use algebraic representation.
Let's assume that Almaz scored x in the first test and y in the second test.
According to the given information, Almaz's average score is 7 out of 10. This means that the sum of her scores divided by the number of tests is equal to 7/10:
(x + y) / 2 = 7/10
We also know that the product of her scores is 45:
x * y = 45
To solve this system of equations, we can use substitution. Rearrange the first equation to solve for x:
x + y = (7/10) * 2
x + y = 1.4
Now substitute this value of (x + y) into the second equation:
(1.4 - y) * y = 45
Simplify the equation:
1.4y - y^2 = 45
Rearrange and rewrite the equation as a quadratic equation:
y^2 - 1.4y + 45 = 0
Now you can solve this quadratic equation using factoring, completing the square, or the quadratic formula to find the values of y. Once you have the values of y, substitute them back into the equation x + y = 1.4 to find the corresponding values of x.
After finding the values of x and y, you will know what Almaz scored in each test.