## Algebra: A Combined Approach (4th Edition)

(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%) $\frac{2+x}{5+22}\geq\frac{7}{10}$ $\frac{2+x}{27}\geq\frac{7}{10}$ $2+x\geq\frac{7\times27}{10}$ $x\geq18.9-2$ $x\geq17.9$ $x\approx18$
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. $x\approx18$