## Elementary Linear Algebra 7th Edition

Published by Cengage Learning

# Chapter 1 - Systems of Linear Equations - Review Exercises - Page 36: 57

#### Answer

The number of touchdowns is 6, extra-point kicks is 6 and field goals is 1.

#### Work Step by Step

Add the scores of both teams to get the total score$\rightarrow 35+10=45$ The number of touchdowns, extra-point kicks, and field goals are unknown but we know the ratio between them. We mark the extra-point kicks as our $x$. There is the same number of touchdowns as extra-point kicks, therefore the number of touchdowns is $x$ as well. There were six times as many touchdowns as field goals which means that the number of field goals can be expressed as $\frac{x}{6}$. Now we have the proportion: $x:x:\frac{x}{6}$ We assign them the points they are worth of and we get $6\times x$ for touchdowns, $1\times x$ for extra-point kicks and $3\times \frac{x}{6}$ for field goals. We know that $6\times x$, $1\times x$ and $3\times \frac{x}{6}$ should be equal to the total points scored which is 45. From these data we can make an equation: $6x+x+\frac{3x}{6}=45$ After simplification we get $x=6$ Using the proportion we can calculate that the number of touchdowns is 6, extra-point kicks is 6 and field goals is 1.

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