The scores on a test are found by adding and subtracting points as shown in table below. If Salazar's score on a 15 question test was 86 points,how many of his answers were correct, incorrect and blank.
Answers Points correct +8 incorrect -4 blank -2
86 divided by 14 = +6, -2, 0 blank
To find out how many of Salazar's answers were correct, incorrect, and blank, we need to calculate the total score and divide it by the corresponding point values.
Let's denote:
C as the number of correct answers,
I as the number of incorrect answers,
and B as the number of blank answers.
The total score on the test is 86. We can represent this as an equation:
C * 8 + I * (-4) + B * (-2) = 86
We also know that the test consists of 15 questions, so we can write:
C + I + B = 15
To solve this system of equations, we can use either substitution or elimination method. Let's use substitution:
From the second equation, we can express B in terms of C:
B = 15 - C
Substituting this into the first equation, we have:
C * 8 + I * (-4) + (15 - C) * (-2) = 86
Simplifying the equation:
8C - 4I - 30 + 2C = 86
10C - 4I = 116
Dividing both sides by 2:
5C - 2I = 58
From here, we can solve for C in terms of I:
C = (58 + 2I)/5
To find integer solutions for C and I, we need to test different values of I and check if it results in a whole number for C.
Let's start by checking I = 1:
C = (58 + 2*1)/5 = 60/5 = 12/1 = 12 (a whole number)
So, if I = 1, then C = 12.
Next, let's check I = 2:
C = (58 + 2*2)/5 = 62/5 = 12.4 (not a whole number)
Therefore, the solution (C, I) = (12, 1) satisfies the system of equations.
Now, we can find B by substituting C = 12 into the second equation:
B = 15 - C = 15 - 12 = 3
So, Salazar has 12 correct answers, 1 incorrect answer, and 3 blank answers.
To find out the number of correct, incorrect, and blank answers, we can use the table provided.
First, let's divide the total score of 86 by the point values. From the table, we know that correct answers add 8 points, incorrect answers deduct 4 points, and blank answers deduct 2 points.
86 divided by 8 (points for correct answers) equals 10.75. This means Salazar got approximately 10 correct answers.
To find the number of incorrect answers, we divide 86 by -4 (points for incorrect answers). This gives us -21.5. Since we can't have a negative number of incorrect answers, we round this down to 21 incorrect answers.
Finally, to determine the number of blank answers, we divide 86 by -2 (points for blank answers). This gives us -43. Since we can't have a negative number of blank answers, we round this down to 43 blank answers.
So, Salazar had approximately 10 correct answers, 21 incorrect answers, and 43 blank answers on the 15-question test.