almaz has taken two tests her average score is 7 (out of ten )the product of her scores is 45. what did she score in each test?
Can you not think of two numbers that add up to 14 and multiply to get 45 ?
To find out what Almaz scored in each test, we can use algebraic equations. Let's assume that her score in the first test is "x" (out of 10) and her score in the second test is "y" (out of 10).
We know that Almaz's average score is 7 (out of 10), so we can set up the equation:
(x + y) / 2 = 7
Next, we are given that the product of her scores is 45 (out of 100). Since the scores are out of 10, we need to multiply the scores by 10 to get them out of 100:
x * y = 45 * 10
Simplifying this equation, we get:
xy = 450
Now we have a system of equations:
(x + y) / 2 = 7
xy = 450
We can solve this system of equations using substitution or elimination. Let's use substitution to solve them.
From the first equation, we can solve for x in terms of y:
x = 14 - y
Substitute this value of x in the second equation:
(14 - y) * y = 450
Expanding and simplifying, we get:
14y - y^2 = 450
Now rearrange the equation to a quadratic equation form:
y^2 - 14y + 450 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring doesn't work, so let's use the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = -14, and c = 450. Substituting these values into the formula:
y = (-(-14) ± √((-14)^2 - 4 * 1 * 450)) / (2 * 1)
Simplifying further:
y = (14 ± √(196 - 1800)) / 2
y = (14 ± √(-1604)) / 2
Since the value inside the square root is negative, it means that there is no real solution for y. Therefore, Almaz's scores cannot be determined based on the given information.
Please note that these calculations assume Almaz's scores are out of 10 and that there are no other factors affecting the scores.