Unit 5

4 marks · Easy

A box contains balls with masses that have been measured to the nearest gram. The total mass of all the balls is 230 g. The number of balls in the box is given by n, which satisfies the equation n^2 - 15n + 54 = 0.

(a)

Write down the lower bound and upper bound for the total mass of the balls.

[1 mark]

(b)

Solve the equation n^2 - 15n + 54 = 0 to find the number of balls in the box.

[2 marks]

(c)

If each ball has approximately the same mass, estimate the average mass of one ball, using the lower bound for the total mass and the larger value of n. Give your answer to the nearest gram.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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(a) Lower bound = 229.5 g, Upper bound = 230.5 g

(b) n = 9 or n = 6

Common mistakes: Not using correct bounds (should be 229.5 g and 230.5 g); Solving the quadratic incorrectly; Incorrect division for estimation

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Correct lower and upper bounds given as 229.5 g and 230.5 g.

M1 (b) · 1 mark · Attempts to solve quadratic equation by factorising or using quadratic formula.

A1 (b) · 1 mark · Both correct solutions for n: n = 9 and n = 6.

A1 (c) · 1 mark · Accurate estimate for lower bound average mass using 229.5 / 9 rounded to nearest gram.

Worked solution

(a) Since 230 g is measured to the nearest gram, lower bound = 230 - 0.5 = 229.5 g, upper bound = 230 + 0.5 = 230.5 g.

(b) Solve n^2 - 15n + 54 = 0: Factorise as (n-9)(n-6)=0, so n = 9 or 6.