Numeracy Intermediate June 2022 Unit 1 Q8
8. People travel by bus or by train from Hiraddug Station.
On Tuesday, 420 people travelled by bus from the station.
(a) Of the 420 people who travelled by bus from the station, 35% had a travel pass.
Calculate the number of people who travelled by bus and did not have a travel pass. [3]
Calculate the number of people who travelled by bus and did not have a travel pass. [3]
(b) On Tuesday, the ratio of the number of people travelling by bus to the number of people travelling by train was 20 : 17.
Calculate the number of people who travelled by train from the station on Tuesday. [3]
Calculate the number of people who travelled by train from the station on Tuesday. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 420 - 420 × 35 ÷ 100 (= 420 – 147) or (100 – 35) × 420 ÷ 100 or equivalent | M2 | M1 for any one of
|
| 273 (people) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| 420 ÷ 20 × 17 | M2 | M1 for any of the following:
|
| 357 (people) | A1 | CAO. Allow embedded as 420 : 357 Award A0 for 357 : 420 |
Alternative method 1
| Scheme | Marks | Comments |
|---|---|---|
| (420 ÷ 20) × (20 + 17) – 420 (= 777 – 420) | M2 | M1 for any of the following:
|
| 357 (people) | A1 | CAO. Allow embedded as 420 : 357 Award A0 for 357 : 420 |
The alternative method is printed in italics in the original.
Alternative method 2
| Scheme | Marks | Comments |
|---|---|---|
| 420 – (20 – 17) × (420 ÷ 20) (=420 – 63) | M2 | M1 for any of the following:
|
| 357 (people) | A1 | CAO. Allow embedded as 420 : 357 Award A0 for 357 : 420 |
The alternative method is printed in italics in the original.
Alternative method 3
| Scheme | Marks | Comments |
|---|---|---|
| Full ratio method to find 357 people, e.g. \((20\ \times)\ \dfrac{420}{(20)} : 17 \times \dfrac{420}{20}\) | M2 | Allow seen in stages, including written as an appropriate sum of equivalent ratios, e.g. attempting 17 + 340 (from 20 : 17 and 400 : 340) M1 for any of the following:
|
| 357 (people) | A1 | CAO. Allow embedded as 420 : 357 Award A0 for 357 : 420 |
The alternative method is printed in italics in the original.