Answers − Ratios
1. Share £400 in the ratio 1 : 3
| (a) | Add the separate parts of the ratio to find the total number of parts 1 + 3 = 4 |
| (b) | Divide 400 by 4 to find the value for each part: 100 |
| (c) | Multiply each term in the ratio by 100: 1 x 100 = 100, 3 x 100 = 300 |
So £400 shared in the ratio 1 : 3 is £100 and £300
2. Divide 225 grams in the ratio 1 : 2
| (a) | Add the separate parts of the ratio to find the total number of parts 1 + 2 = 3 |
| (b) | Divide 225 by 3 to find the value for each part: 75 |
| (c) | Multiply each term in the ratio by 75: 1 x 75 = 75, 2 x 75 = 150 |
So £225 shared in the ratio 1 : 2 is £75 and £150
3. Share £560 in the ratio 3 : 5
| (a) | Add the separate parts of the ratio to find the total number of parts 3 + 5 = 8 |
| (b) | Divide 560 by 8 to find the value for each part: 70 |
| (c) | Multiply each term in the ratio by 70: 3 x 70 = 210, 5 x 70 = 350 |
So £560 shared in the ratio 3 : 5 is £210 and £350
4. Divide 270 kg in the ratio 2 : 7
| (a) | Add the separate parts of the ratio to find the total number of parts 2 + 7 = 9 |
| (b) | Divide 270 by 9 to find the value for each part: 30 |
| (c) | Multiply each term in the ratio by 30: 2 x 30 = 60, 7 x 30 = 210 |
So 270 kg shared in the ratio 2 : 7 is 60 kg and 210 kg
5. Share £440 in the ratio 3 : 8
| (a) | Add the separate parts of the ratio to find the total number of parts 3 + 8 = 11 |
| (b) | Divide 440 by 11 to find the value for each part: 40 |
| (c) | Multiply each term in the ratio by 12: 3 x 40 = 120, 8 x 40 = 320 |
So £440 shared in the ratio 3 : 8 is £120 and £320
6. The cost of a weekend break is divided between two families in the ratio of 3 : 7 the smaller share was £90. How much is the total cost of the weekend break?
| (a) | Add the separate parts of the ratio to find the total number of parts 3 + 7 = 10 |
| (b) | 3/10 of the cost was £90, so 1/10 is £30 |
| (c) | The total cost is: 10 x £30 = £300 |
So the total cost is £300
7. The cost of a holiday is divided between two families in the ratio of 3 : 8 the smaller share was £240. How much is the total cost of the holiday?
| (a) | Add the separate parts of the ratio to find the total number of parts 3 + 8 = 11 |
| (b) | 3/11 of the cost was £240, so 1/11 is £80 |
| (c) | The total cost is: 11 x £80 = £880 |
So the total cost is £880
8. The ratio of male teachers to female teachers is 2 : 7. If there are 84 female teacher, how many male teachers are there?
| (a) | Add the separate parts of the ratio to find the total number of parts 2 + 7 = 9 |
| (b) | So 7/9 are female teachers is 84, so 1/9 is 12 |
| (c) | The number of male teachers: 2 x 12 = 24 |
So the total number of male teachers is 24
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