Intermediate November 2016 Unit 1 Q17
17. William has \(n\) marbles.
Lois had 4 times as many marbles as William, but she has now lost 23 of them.
Lois still has more marbles than William.
Write down an inequality in terms of \(n\) to show the above information.
Use your inequality to find the least number of marbles that William may have. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \(4n - 23 \gt n\) or \(n \lt 4n - 23\) or equivalent. | B2 | B1 for 4n ± …. > n OR B1 for 4n – 23 > an + b a≠0. OR B1 for 4n – 23 ≥ n. B0 for 4n – 23 < n |
| (least number of marbles =) 8 | B2 | F.T. from ‘their inequality’, if of equivalent difficulty. (e.g. 4n – 23 > n + 23 giving an answer of 16) B1 for sight of \(n \gt \dfrac{23}{3}\) or equivalent. (With similar F.T. answer e.g. n > 46/3 from above example of 4n – 23 > n + 23) OR allow B1 for n > 7 OR n ≥ 8 (With similar F.T. answer e.g. n > 15 from above example of 4n – 23 > n + 23) |