Question

Sam and Alex play in the same soccer team. Last saturday Alex scored $3$ more goals than Sam, but together they scored less than $9$ goals. What are the possible number of goals that Alex scored?

• A. $5$
• B. $3$
• C. $6$
• D. $4$

Answer 1

Answer: (A), (B), (D)

$4$

Given: Last saturday Alex scored $3$ more goals than Sam, but together they scored less than $9$ goals

Let number of goals scored by Alex be $A$ and goals scored by Sam be $S$

Alex scored $3$ more goals than Sam $\Rightarrow A=S+3\cdots \left(i\right)$
Together they scored less than $9$ goals $\Rightarrow A+S<9\cdots \left(ii\right)$

From $\left(i\right),\left(ii\right)$
$S+S+3<9$
$\Rightarrow 2S+3<9$
$\Rightarrow 2S+3-3<9-3\left[\text{subtract}3\text{from both the side of inequality}\right]$
$\Rightarrow 2S<6$
$\Rightarrow \frac{2S}{2}<\frac{6}{2}\left[\text{divide both the sides by}2\right]$
$\Rightarrow S<3$
$\Rightarrow S=0,1,2\left[\text{Goals can not be negative}\right]$

As $A=S+3$,
For $S=0,1,2\Rightarrow A=3,4,5\text{respectively.}$


$$\begin{array}{cccc}S& A=S+3& S+A& S+A<9\\ 0& 3& 3& ✓\\ 1& 4& 5& ✓\\ 1& 5& 7& ✓\\ 3& 6& 9& \times \times \end{array}$$