Question

# Eastside Golden Eagles scored 60 points on a combi:nation of tWo-polnt shots and three-point shots. If theymade a total of 27 shots. how many of each kind ofshot was made”?

Upper level algebra
Eastside Golden Eagles scored 60 points on a combi: nation of two-polnt shots and three-point shots. If they made a total of 27 shots. how many of each kind of shot was made&rdquo;?

2021-03-03

suppose that
number of 2 point shots is N2
number of 3 points shots is N3
thus
$$\displaystyle{N}{2}+{N}{3}={27}----------{\left({g}{i}{v}{e}{n}\right)}$$
so
$$\displaystyle{N}{2}={27}-{N}{3}-----------{\left({1}\right)}$$
scored point of 2 point shots = 2 N2
scored point of 3 point shots = 3 N3
thus
$$\displaystyle{2}{N}{2}+{3}{N}{3}={60}--------{\left({2}\right)}{\left({g}{i}{v}{e}{n}\right)}$$
compensate by N2 = 27 - N3 in ( 2 )
$$\displaystyle{2}{\left({27}-{N}{3}\right)}+{3}{N}{3}={60}$$
$$\displaystyle{54}-{2}{N}{3}+{3}{N}{3}={60}$$
$$\displaystyle{54}+{N}{3}={60}{\left({a}{d}{d}-{54}\ to\ both\ {s}{i}{d}{e}{s}\right)}$$
$$\displaystyle{N}{3}={60}-{54}={6}$$
compensate in ( 1 ) by $$N3 = 6$$
$$\displaystyle{N}{2}+{6}={27}{\left({a}{d}{d}-{6}\ to\ both\ {s}{i}{d}{e}{s}\right)}$$
$$\displaystyle{N}{2}={27}-{6}={21}$$
thus
$$\displaystyle{N}{2}={21}{\quad\text{and}\quad}{N}{3}={6}$$