Chapter 1.3, Problem 37PPE

a.

To determine

To find : An expression that describes the number of points scored on touchdowns T and points after touchdowns p by one team in a game.

Answer to Problem 37PPE

An expression is given by:

  $6\times T=p$

Explanation of Solution

Given information :  1 Touchdown is awarded 6 points

In the expression, touchdown T is multiplied with 6 which give the points scored by the touchdowns. By using this expression, one can calculate the number of points scored after touchdown. T here refers to the number of touchdowns.

For example, if the number of touchdowns =4

Then, total points scored,

  $\begin{array}{c}p=6\times 4\\ =24\end{array}$

Therefore, the expression is given by:

  $6\times T=p$

b.

To determine

To find :  An equation to represent the possible number of touchdowns and points after touchdowns by the winning team.

Answer to Problem 37PPE

  $y=\frac{x}{6}$

Explanation of Solution

Given information :  A team wins a football game by 27-0.

Calculation : 

In this, total numbers of touchdowns are calculated from the given score.

Thus, by putting the value of x (total score) in the expression, total number of touchdowns is obtained that is equal to 4.

  $x=27$

Hence, $y=\frac{27}{6}$

In the expression, total number of touchdowns is obtained by dividing the total score obtained by 6 as 1 touchdown is equal to 6 points.

The equation to represent the possible number of touchdowns and points after touchdowns by the winning team.

  $y=\frac{x}{6}$

c.

To determine

To calculate :  Possible number of touchdowns and points after touchdowns by both teams after the game.

Answer to Problem 37PPE

  $\text{Possible number of touchdowns by one team }=3$

And, $\text{points after 3 touchdowns }=18$

  $\text{Possible number of touchdowns by another team }=1$

And, $\text{points after 1 touchdown }=6$

Explanation of Solution

Given information :  Team score 21-7

Formula used : 

possible number of touchdowns = $\frac{\left(\text{Total points scored }\right)}{6}$

And points after touchdowns = $n\times 6$

Where, $n=\text{ number of touchdowns}$

Calculation :  For one team,

  $\text{Score}=21\text{ points}$

Thus, possible number of touchdowns $=\frac{21}{6}$

  $=3$

And points after 3 touchdowns $=6\times 3$

  $\text{=18}$

For another team,

  $\text{Score}=7\text{ points}$

Thus, possible number of touchdowns $=\frac{7}{6}$

  $\text{=1}$

And $\text{points after 1 touchdown }=6\times 1$

  $\text{= 6}$

In this, total number of touchdowns and points after touchdowns for two teams is calculated by putting the values in the formula.

Total number of touchdowns scored by 1 team is equal to 3 and the points scored after touchdown is 18. Remaining 3 points are scored by kicking.

Total number of touchdowns scored by another team is equal to 1 and the points scored after touchdown is 6. Remaining 1 point is scored by kicking