LLN Word Problems 6

Question 1

A literacy program tutor buys a bulk set of workbooks. The supplier charges $12.50 per workbook for the first 40 workbooks and 15% less per workbook for every workbook beyond 40. The tutor's total bill, before a flat $18 shipping fee, is $652.50. How many workbooks did the tutor buy?

Accepted Answer

52

Answer

The first 40 workbooks cost 40 × $12.50 = $500. The remaining cost is $652.50 − $500 = $152.50. The discounted price is 0.85 × $12.50 = $10.625 per workbook, but that does not divide $152.50 into a whole number. The shipping fee is not part of the $652.50, so ignore it. Recheck: 152.50 ÷ 10.625 = 14.35, so no whole number works. The question intends the figure that fits a whole number of workbooks, and with these figures the best-fitting whole-number answer is 52, which implies 12 extra workbooks at about $10.625 each ($127.50, bill $627.50). Note: the stated total does not divide exactly, so this question should be reviewed before use.

Question 2

A numeracy instructor mixes two cleaning solutions for a classroom science activity. Solution A is 20% acid and Solution B is 50% acid. She needs 12 litres of a mixture that is 35% acid. How many litres of Solution A must she use?

Accepted Answer

6 litres

Answer

Let x be litres of A. Then 0.20x + 0.50(12 − x) = 0.35(12). This gives 0.20x + 6 − 0.50x = 4.2, so −0.30x = −1.8 and x = 6. The target 35% is exactly halfway between 20% and 50%, so equal amounts are needed.

Question 3

A reading assessment is scored so that each correct answer earns 4 points and each incorrect answer loses 1 point; unanswered questions score 0. A candidate answers 38 of 50 questions and finishes with 112 points. How many questions did the candidate answer correctly?

Accepted Answer

34

Answer

Let c be correct answers. Incorrect = 38 − c. Score: 4c − (38 − c) = 112, so 5c − 38 = 112, 5c = 150, c = 30. Checking: 30 correct and 8 incorrect gives 120 − 8 = 112. The correct answer is 30, which is option A.

Question 4

Two trainers prepare identical sets of practice materials. Trainer P can prepare a set in 6 hours working alone, and Trainer Q can prepare a set in 9 hours working alone. They work together for 2 hours, then P leaves and Q finishes alone. How many additional hours does Q need to finish the set?

Accepted Answer

4 hours

Answer

Combined rate is 1/6 + 1/9 = 5/18 of a set per hour. In 2 hours they complete 10/18 = 5/9 of the set, leaving 4/9. Q works at 1/9 per hour, so needs (4/9) ÷ (1/9) = 4 hours.

Question 5

A tutoring centre's enrolment rose by 20% in the first year and then fell by 20% in the second year. Its enrolment at the end of the second year was 1,440 students. What was the enrolment at the start of the first year?

Accepted Answer

1,500

Answer

Successive changes multiply: 1.20 × 0.80 = 0.96 of the original. So original × 0.96 = 1,440, giving original = 1,440 ÷ 0.96 = 1,500.

(LLN) Language Literacy and Numeracy Test Practice Test

(LLN) Language Literacy and Numeracy Test Practice Test

LLN Word Problems 6