Almaz Has Taken 2 Tests.Her Average Score Is 7 Out Of 10.The product Of Her Scores Is 45.What Did She Score In Each Test?
5*9 = 45
No idea
Let's assume that Almaz scored x out of 10 on her first test and y out of 10 on her second test.
According to the given information, Almaz's average score is 7 out of 10. So, we can write the equation: (x + y) / 2 = 7.
The product of her scores is 45. So, we can write the equation: x * y = 45.
To solve these equations, we can use substitution or elimination method.
Using substitution method:
From the first equation, x + y = 14 (by multiplying both sides by 2).
Now, substitute the value of x from the second equation into the first equation:
x = 45 / y
Substituting this value in the first equation:
45 / y + y = 14
Multiplying both sides by y:
45 + y^2 = 14y
Rearranging the equation:
y^2 - 14y + 45 = 0
Factoring the quadratic equation:
(y - 9)(y - 5) = 0
So, y = 9 or y = 5.
If y = 9, then x = 45 / 9 = 5.
If y = 5, then x = 45 / 5 = 9.
Therefore, Almaz scored 5 out of 10 on her first test and 9 out of 10 on her second test, or vice versa.
To find out what Almaz scored in each test, let's call her scores on the first and second test x and y, respectively.
We know that the average score is 7 out of 10, so we can set up the equation:
(x + y)/2 = 7
Now, let's solve for x + y:
x + y = 7 * 2
x + y = 14 ----- Equation 1
We are also given that the product of her scores is 45:
x * y = 45 ----- Equation 2
Now we have a system of equations. We can solve this system by substitution or elimination method.
Let's solve using the substitution method. We'll isolate one variable in Equation 1 and substitute into Equation 2:
From Equation 1, we can isolate x:
x = 14 - y
Now substitute x into Equation 2:
(14 - y) * y = 45
Expanding the equation:
14y - y^2 = 45
Rearranging the equation:
y^2 - 14y + 45 = 0
This equation is a quadratic equation. We can solve it by factoring or using the quadratic formula.
Factoring:
(y - 5)(y - 9) = 0
Setting each factor equal to zero:
y - 5 = 0 or y - 9 = 0
y = 5 or y = 9
Now, substitute the values of y back into Equation 1 to solve for x:
For y = 5:
x + 5 = 14
x = 14 - 5
x = 9
For y = 9:
x + 9 = 14
x = 14 - 9
x = 5
So, Almaz scored 9 on the first test and 5 on the second test, or vice versa.