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Worked solution

Basketball: distinguish attempts, successes and points

In basketball, points are scored by a successful free throw or a field goal. A successful free throw is worth 1 point while a field goal is worth either 2 or 3 points. An attempt can either be a free throw attempt or a field goal attempt.

In the recently concluded basketball season, Stephen had 1695 attempts in total. 60% of these attempts were successful and he scored a total of 1917 points. 40% of his successful free throws and 25% of his field goal points were scored during the second half of the season, where Stephen scored a total of 534 points.

Calculate the number of 2-point field goals during the season. marks

[2016/NJC/Promo/3]

CJC · Review Problems · Question 5

Answer

404 two-point field goals.

Count successful attempts

The number of successful attempts is 0.6(1695)=10170.6(1695)=1017. Let x,y,zx,y,z count successful free throws, 2-point goals and 3-point goals. Then x+y+z=1017x+y+z=1017.

How did this part go?

Count total and second-half points

Total points give x+2y+3z=1917x+2y+3z=1917. Second-half points give 0.4x+2(0.25)y+3(0.25)z=5340.4x+2(0.25)y+3(0.25)z=534, or 0.4x+0.5y+0.75z=5340.4x+0.5y+0.75z=534. The 25% applies to field-goal points, so the factors 2 and 3 remain.

How did this part go?

Solve and answer the requested category

The source GC solution is x=365,y=404,z=248x=365,y=404,z=248. Check 365+404+248=1017365+404+248=1017, 365+2(404)+3(248)=1917365+2(404)+3(248)=1917, and 0.4(365)+0.5(404)+0.75(248)=5340.4(365)+0.5(404)+0.75(248)=534. There were 404 successful 2-point field goals.

How did this part go?

Common mistakes

Successful attempts are not total points. A three-point basket is one success but three points.

Solution notes

Also printed as Review 5 in both CJC Linear Equations lecture copies: question PDF page 14 / printed 174; answer PDF 15 / Student printed 175, Teacher visible footer 15 (extracted 175). Compared in evidence/review-cjc-linear-equations-lecture.md; the repeated asks, tables and marks retain this existing identity.

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