Answer
(a) (50%)
$\frac{2+x}{5+22}\geq\frac{1}{2}$
$\frac{2+x}{27}\geq\frac{1}{2}$
$2+x\geq\frac{1\times27}{2}$
$x\geq13.5-2$
$x\geq11.5$
$x\approx12$
(b) (70%)
$\frac{2+x}{5+22}\geq\frac{7}{10}$
$\frac{2+x}{27}\geq\frac{7}{10}$
$2+x\geq\frac{7\times27}{10}$
$x\geq18.9-2$
$x\geq17.9$
$x\approx18$
Work Step by Step
We have to ensure that the total number of shots made divided by the total number of shots attempted (the total number of shots made + the total number of shots missed) is AT LEAST 50%, or $\frac{1}{2}$. This means that we have to score a minimum of 50%, so we use the inequality sign $\geq$
Hence, we use the following equation:
$\frac{2+x}{5+22}\geq\frac{1}{2}$
$\frac{2+x}{27}\geq\frac{1}{2}$
$2+x\geq\frac{1\times27}{2}$
$x\geq13.5-2$
$x\geq11.5$
Since the answer has to be a whole number of shots, as we cannot possibly make half a shot, x rounds up to 12.
$x\approx12$
Doing the same thing for 70%, which is also $\frac{7}{10}$
$\frac{2+x}{5+22}\geq\frac{7}{10}$
$\frac{2+x}{27}\geq\frac{7}{10}$
$2+x\geq\frac{7\times27}{10}$
$x\geq18.9-2$
$x\geq17.9$
Since the answer has to be a whole number of shots, as we cannot possibly make 0.9 of a shot, x rounds up to 18.
$x\approx18$
