almaz has teken two tests.her average score is 7(out of ten). the product of her scores is 45. what did she score in each test?
xy=45
x+y=14 or x=14-y
(14-y)y=45
y^2-14y+45=0
y=9 or 5
Factors of 45:
1 * 45
3 * 15
5 * 9
Which of those pairs of factors would produce an average of 7?
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Well, Almaz must be feeling pretty average with those scores! But let's see if we can figure out what she scored in each test. Since her average score is 7, and she took two tests, the total sum of her scores must be 7 x 2 = 14. Now, since the product of her scores is 45, we can set up the equation:
x * y = 45
And we know that x + y = 14. So, we have a system of equations. Hmm, this feels a bit like "test-geometry" to me! Let me put on my thinking cap...
*Clown Bot puts on a giant, polka-dotted thinking cap*
After some clownish calculations, I found that Almaz scored a 9 on one test and a 5 on the other! Ta-da! Almaz really knocked one test out of the park while the other one gave her a bit of a colorful surprise.
To find out what Almaz scored in each test, we can set up a system of equations based on the given information.
Let's represent Almaz's scores on the first and second test as x and y, respectively.
We know that the average score is 7 out of 10, so the sum of the scores divided by 2 (the number of tests) should equal 7:
(x + y) / 2 = 7 -- Equation 1
We also know that the product of her scores is 45:
x * y = 45 -- Equation 2
To solve this system of equations, we can use substitution or elimination method.
Let's solve it using the substitution method:
From Equation 1, we can isolate one variable (x or y) and substitute it into Equation 2.
Rearranging Equation 1, we have:
x + y = 14
Solving for y, we get:
y = 14 - x
Substituting this value of y in Equation 2, we have:
x * (14 - x) = 45
Expanding and rewriting the equation, we get:
14x - x^2 = 45
Rearranging to a quadratic equation form:
x^2 - 14x + 45 = 0
Now we can solve this quadratic equation to find the values of x (the score on the first test).
Factoring the quadratic equation, we have:
(x - 5)(x - 9) = 0
This equation has two solutions:
x - 5 = 0 --> x = 5
x - 9 = 0 --> x = 9
Since we have two possible values for x, we need to calculate the corresponding values of y using Equation 1.
When x = 5:
y = 14 - x
y = 14 - 5
y = 9
When x = 9:
y = 14 - x
y = 14 - 9
y = 5
Therefore, Almaz scored 5 in the first test and 9 in the second test.
So, Almaz scored 5 out of 10 on the first test and 9 out of 10 on the second test.