# Question ffe8d

Sep 27, 2016

Here's what I got.

#### Explanation:

The idea here is that we can use the information provided by the problem to create a system of two equations with two unknowns, the number of victories, let's say $x$, and the number of ties, let's say $y$.

For starters, we know that in their championship season, they won $9$ more games than they tied, so

$x = y + 9 \text{ " " } \textcolor{\mathmr{and} a n \ge}{\left(1\right)}$

We also know that the team gets $2$ points for a win and $1$ point for a tie, and that they accumulated a total of $60$ points in their championship season.

We can thus say that

overbrace(2 * x)^(color(blue)("points coming from wins")) + overbrace(1 * y)^(color(purple)("points coming from ties")) = 60" " " "color(orange)((2))

We now have two equations with two unknowns. Take the value of $x$ from equation $\textcolor{\mathmr{and} a n \ge}{\left(1\right)}$ and plug it into equation $\textcolor{\mathmr{and} a n \ge}{\left(2\right)}$

$2 \cdot \left(y + 9\right) + y = 60$

Solve this for $y$

$2 y + 18 + y = 60$

$3 y = 42 \implies y = 14$

This means that $x$ will be

$x = 14 + 9 = 23$

Therefore, we can say that the team won $23$ games and tied $14$ games.

Sep 27, 2016

$23 \text{ games won and " 14 " tied}$

#### Explanation:

Stefan V has answered this question using 2 variables to form 2 equations and then solving them simultaneously .

It is also possible to solve by using only one variable.
Define one quantity and then write the other quantity in terms of the first.

The team won more games than they tied.

Let the number of games tied be $\textcolor{b l u e}{x} \text{ } \leftarrow$. smaller number

The number of games won is $\left(\textcolor{red}{x + 9}\right) \text{ } \leftarrow$ they won 9 more.

2 points were given for each win: (color(red)(2(x+9))#
1 point was given for each tie. $\left(\textcolor{b l u e}{1 \times x}\right)$

The total number of points was 60.

$2 \left(x + 9\right) + x = 60$

$2 x + 18 + x = 60$

$3 x + 18 = 60$

$3 x = 42$

$x = 42 \div 3 = 14$

$14 \text{ games were tied }$

$14 + 9 = 23 \text{ games were won }$

Check: $2 \times 23 + 1 \times 14$

$= 46 + 14 = 60$