In a math contest of 10 problems, 5 points were given for each correct answer and 2 points were deducted for each incorrect answer. If Nancy answered all 10 problems and scored 29 points, how many correct answers did she have?

Nancy had 7 correct answers.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.  Let's assign the variable c to represent the number of correct answers Nancy had and the variable i represent the number of incorrect answers she had.

We know that the total number of answers is 10 because it is given that she answered all 10 problems.  This lets us set up the first equation as follows:

c + i = 10

Then, we can set up a second equation using the number of points (29 total).  We know that +5 points were added for each correct response (c) and -2 points were added for each incorrect response (i).  Our next equation will look like this:

5c - 2i = 29

There are many different strategies one can use to solve systems of equations.  In this case, I am going to use combination.  This means I am going to add the two equations together.  However, first I should multiply our first equation by 2 so that the "I" variable terms cancel out.  This is modeled below:

2c + 2i = 20

Now we can add the two equations:

5c + 2c +2i - 2i = 20 +29

Now we can simplify the equation by combining the like terms to get:

7c = 49

Finally, we should divide both sides of the equation by 7 in order to get the variable c by itself on the left side of the equation.

c = 7

Therefore, the correct number of responses Nancy gave was 7.

Hope this helps!

sorry, i can't understand your question. will later if you describe more clearly!

: )

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24