Question

1. football a field goal is 3 points and the extra point after a touchdown is 1 point. in a recent season, dan bailey of the dallas cowboys made a total of 66 field goals and extra points for 124 points. find the number of field goals and extra points that he made.
2. three times the sum of the two numbers is 36. what are the two numbers?

number theory four times a number minus 5 times another number is equal to

Explanation:

Problem 20

Step1: Define variables

Let $x$ = number of field goals, $y$ = number of extra points.

Step2: Set up equations

Total kicks: $x + y = 66$
Total points: $3x + y = 124$

Step3: Subtract first equation

Subtract $x + y = 66$ from $3x + y = 124$:
$$(3x + y) - (x + y) = 124 - 66$$
$$2x = 58$$

Step4: Solve for x

$$x = \frac{58}{2} = 29$$

Step5: Solve for y

Substitute $x=29$ into $x + y = 66$:
$$29 + y = 66$$
$$y = 66 - 29 = 37$$

Step1: Define variables

Let $a$ = first number, $b$ = second number.

Step2: Set up equations

$4a - 5b = 3(a + b)$
$a + b = 36$

Step3: Simplify first equation

$$4a - 5b = 3a + 3b$$
$$4a - 3a = 3b + 5b$$
$$a = 8b$$

Step4: Substitute into sum equation

Substitute $a=8b$ into $a + b = 36$:
$$8b + b = 36$$
$$9b = 36$$

Step5: Solve for b

$$b = \frac{36}{9} = 4$$

Step6: Solve for a

$$a = 8 \times 4 = 32$$

Answer:

Number of field goals: 29; Number of extra points: 37

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Problem 21