Higher November 2019 Paper 1 Q16
16 In a box there are some buttons.
45 are large and the rest are small.
Some are yellow and the rest are green.
The number of small is \(\dfrac{5}{3}\) of the number of large.
The number of green is 300% of the number of yellow.
There are 12 small yellow buttons.
How many large green buttons are there?
You may use the two-way table to help you. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(45 \times \dfrac{5}{3}\) or 75 | M1 | 75 seen as total of Small column implied by 120 seen as overall total |
| (their \(75 + 45) \div (1 + 3)\) or \(120 \div 4\) or 30 (Yellow) | M1dep | 30 seen as total of Yellow row |
| their \(30 - 12\) or 18 (Large Yellow) | M1dep | 18 in Large Yellow cell |
| 27 | A1 | Accept 27 in correct cell if answer blank |
| Alternative method 2 | ||
| \(45 \times \dfrac{5}{3}\) or 75 | M1 | 75 seen as total of Small column implied by 120 seen as overall total |
| their \(75 - 12\) or 63 (Small Green) | M1dep | 63 in Small Green cell |
| (their \(75 + 45) \div (1 + 3) \times 3\) or \(120 \div 4 \times 3\) or 90 (Green) | M1dep | dep on first M1 90 seen as total of Green row |
| 27 | A1 | Accept 27 in correct cell if answer blank |
| Alternative method 3 | ||
| \(45 \times \dfrac{5}{3}\) or 75 | M1 | 75 seen as total of Small column implied by 120 seen as overall total |
| their \(75 - 12\) or 63 (Small Green) | M1dep | 63 in Small Green cell |
| their \(63 + x = 3(45 - x + 12)\) | M1dep | oe \(\quad 63 + x = 171 - 3x\) |
| 27 | A1 | Accept 27 in correct cell if answer blank |
Additional guidance
In alt 2, 90 only implies M1M0M1 – 63 is also needed for M1M1M1