A bag contains 150 jelly beans. Some of them are red and the rest are blue. The ratio of red to blue jelly beans is `2:3`.
Sophie eats 10 of each colour.
What is the new ratio of red to blue jelly beans?
- `2:3`
- `4:9`
- `5:8`
- `11:17`
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A bag contains 150 jelly beans. Some of them are red and the rest are blue. The ratio of red to blue jelly beans is `2:3`.
Sophie eats 10 of each colour.
What is the new ratio of red to blue jelly beans?
`C`
`text{Original ratio}\ = 2:3`
`text{5 parts = 150}\ \ =>\ \ text{1 part}\ = 150/5=30`
`text{Original ratio (by number)}\ = 2 xx 30:3 xx 30 = 60:90`
`text{After eating 10 of each colour:}`
`text{Ratio}\ = 50:80 = 5:8`
`=>C`
A full container has 4.8 L of a mixture of cordial and water in the ratio 1:3.
After removing 1.2 L of the mixture, more water is added to refill the container.
What is the ratio of cordial to water in the final mixture? (3 marks)
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`3:13`
`text{Original mixture ratio}`
`text{C : W = 1.2 litres : 3.6 litres}`
`text{Removing 1.2 L of mixture, removes}`
`text{→ 300 mL cordial and 900 mL water}`
`text{Cordial in mixture after refill}`
`=1200-300`
`=900\ text{mL}`
`text{Water in mixture after refill}`
`=3600-900+1200`
`=3900\ text{mL}`
`:.\ text{C : W (final mixture)}`
`=900:3900`
`=3:13`
What is 20 minutes to one-third of a day, expressed as a ratio in simplest form?
`B`
`text{Minutes in}\ 1/3\ text{day}`
`=1/3 xx 24 xx 60`
`=480`
`text{Ratio}\ = 20:480 = 1:24`
`=>B`
A total of 11 400 people entered a running race. The ratio of professional runners to amateurs was `3 : 16`. All the professional runners completed the race while 600 of the amateurs did not complete the race.
For those who completed the race, what is the ratio, in its simplest form, of professional runners to amateurs?
`B`
`3:16 =>\ text(Total parts = 19)`
`text(Number of professionals) = 3/19 xx 11\ 400 = 1800`
`text(Number of amateurs) = 16/19 xx 11\ 400 = 9600`
`text(Amateurs who finished) = 9600 – 600 = 9000`
`:.\ text{Ratio of professionals : amateurs (who finished)}`
`= 1800 : 9000`
`=1:5`
`=> B`
A dog breeder owns 500 dogs.
150 are Ridgebacks and the rest are Pugs.
What is the ratio of Ridgebacks to Pugs?
`B`
`text(S)text(ince 150 are ridgebacks,)`
`=> 500-150=350\ text(pugs)`
`text(Ridgebacks)` | `:\ text(Pugs)` |
`150` | `: 350` |
`3` | `: 7` |
`=> B`
There are 48 people in a meeting room.
The ratio of females to males in the room is 13 to 11.
How many females need to leave the room so that the ratio of females to males in the room is 1 to 1? (2 marks)
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`4\ text(females)`
`text(Females : Males) = 13 : 11`
`text(S)text(ince there are 48 people in the room,)`
`26\ text(females : 22 males.)`
`:. 4\ text(females need to leave for the ratio to become 1 : 1)`
Andrew, Brandon and Cosmo are the first three batters in the school cricket team. In a recent match, Andrew scored 30 runs, Brandon scored 25 runs and Cosmo scored 40 runs.
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a. | `A:B:C` | `= 30:25:40` |
`= 6:5:8` |
b. | `text(Total runs by)\ A,B,C` | `= 30 + 25 + 40` |
`= 95` |
`text(Let)\ R` | `=\ text(team runs)` |
`R/95` | `= 36/19` |
`:. R` | `= (36 xx 95)/19` |
`= 180\ text(runs)` |
A potting mix is made up of two ingredients, potting soil and manure, in the ratio 5:2.
21 kilograms of potting mix are used to fertilise the rectangular vegetable garden pictured below.
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i. `text(Potting mix: 21 kg ⇒ 21, 000 grams)`
`text(Area of garden)` | `= 20 xx 7` | |
`= 140\ text(m²)` |
`:.\ text(Rate)` | `= (21\ 000)/140` |
`= 150\ text(g/m²)` |
ii. `text(Ratio 5 : 2)\ \ =>\ \ 5/7 : 2/7`
`:.\ text(Amount of manure)` | `= 2/7 xx 21` |
`= 6\ text(kg)` |
In a raffle, the total prize money is shared among the first two tickets drawn in the ratio 6 : 4.
The prize for the second ticket drawn is $360.
What is the total prize money? (2 marks)
`$900`
`4/10 xx text(Total prize money = $360)`
`=> 1/10 xx text(Total prize money = $90)`
`:.\ text(Total prize money)` | `= 90 xx 10` |
`= $900` |
There are 8 male chimpanzees in a community of 24 chimpanzees.
What is the ratio of males to females in the community?
`=>\ text(B)`
`text(Males)` | `:\ text(Females)` |
`8` | `: (24 – 8)` |
`8` | `: 16` |
`1` | `: 2` |
`=>\ text(B)`
Joel mixes petrol and oil in the ratio 40 : 1 to make fuel for his leaf blower.
How much oil should he add to the petrol to ensure that the fuel is in the correct ratio? (1 mark)
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He wishes to use this fuel in his lawnmower. However, his lawnmower requires the petrol and oil to be mixed in the ratio 25 : 1.
How much oil should he add to the container so that the fuel is in the correct ratio for his lawnmower? (3 marks)
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i. | `text(Petrol : Oil) = 40\ :\ 1` |
`5\ text(Litres :)\ X = 40\ :\ 1` |
`:. 5/X` | `= 40/1` |
`40X` | `=5` |
`X` | `= 5/40 = 0.125\ text(L)` |
`:.\ text(Joel should add 0.125 L of oil)`
ii. `text(4.1 L)\ = 4100\ text(mL)`
`text(In ratio 40:1, there is)`
`=>\ text(4000 mL Petrol and 100 mL Oil)`
`text(Lawnmower ratio) = 25:1`
`text(Let Oil required for 4000 mL Petrol)\ = X\ text(mL)`
`X/4000` | `=1/25` |
`25X` | `=4000` |
`X` | `=4000/25` |
`=160\ text(mL)` |
`text(4 L of petrol requires 160 mL of oil)`
`text(Container already has 100 mL of oil)`
`:.\ text(Oil to add)\ ` | `=160\ -100` |
`=60\ text(mL)` |