Aussie Maths & Science Teachers: Save your time with SmarterEd
A little athletics club is established in a town.
In the first week, 5 girls and 6 boys joined the club.
In the second week, another 4 boys and some more girls joined the club.
The number of girls in the club was now double the number of boys.
How many girls joined the club in the second week?
| 7 | 15 | 17 | 20 |
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`15`
`text(1st week → 6 boys.)`
`text(2nd week → 6 + 4 = 10 boys.)`
`text(Total girls in 2nd week)`
`= 2 xx 10`
`= 20`
`:.\ text(Girls joining in 2nd week)`
`= 20 – 5`
`= 15`
A school has 360 students.
The ratio of boys to girls is 4 to 6.
How many boys attend the school?
| `90` | `144` | `216` | `240` |
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`144`
`text(Ratio is 4 : 6)`
`1/10 xx 360 = 36`
`⇒\ text(Ratio can also be expressed:)`
| `4 xx 36:` | `6 xx 36` |
| `144:` | `216` |
`:. 144\ text(boys attend the school.)`
In a class of 28 students, the ratio of boys to girls is 3 : 4.
Two boys and one girl leave the class. No student joins the class.
What is the new ratio of boys to girls?
`2 : 3`
| `text(Original ratio)\ \ \ 3` | `: 4` |
| `12\ text(boys)` | `: 16\ text(girls)` |
`text(After students leave, new ratio is:)`
| `10` | `: 15` |
| `2` | `: 3` |
Shelly and Carly collect dolls.
The ratio of the number of dolls Shelly owns compared to Carly is 3 : 2.
Shelley owns 12 dolls.
How many dolls does Carly own?
| `2` | `6` | `8` | `18` |
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`8`
`text(Ratio 3 : 2)`
`text(Let)\ \ x=\ text(Number of Carly’s dolls)`
| `x/12` | `= 2/3` |
| `x` | `= (2 xx 12)/3` |
| `= 8\ text(dolls)` |
In a hospital, there are 40 nurses and 600 patients.
What is the ratio of nurses to patients?
| `2:3` | `1:15` | `30:2` | `1:16` |
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`1:15`
| `text(Ratio)` | `=40:600` |
| `=1:15` |
In a class there are 36 students.
The ratio of right handed students to left handed students is 7 : 2.
How many students in the class are left handed?
| `2` | `4` | `8` | `9` |
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`8`
`text(7:2 means that out of 9 students in the class,)`
`text(2 are left handed.)`
`=>\ text(If 18 in class, 4 are left handed)`
`=>\ text(If 27 in class, 6 are left handed)`
`=>\ text(If 36 in class, 8 are left handed)`
John and Fiona each bought a quantity of the same prawns from the fish markets.
John bought a quarter of the quantity that Fiona bought.
The total cost of John and Fiona's prawns was $30.60.
What was the cost of Fiona's prawns?
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`$24.48`
`text(Strategy 1)`
`text(Ratio of prawns)`
`text(Fiona : John = 4 : 1)`
`$30.60 -: 5 = $6.12`
`:.\ text(C)text(ost of Fiona’s prawns = 4 × $6.12 = $24.48`
`text(Strategy 2)`
| `text(Let)\ \ \ p` | `=\ text(cost of John’s prawns)` |
| `:. 4p` | `=\ text(cost of Fiona’s prawns)` |
| `p + 4p` | `= 30.60` |
| `5p` | `= 30.60` |
| `p` | `= $6.12` |
`:.\ text(Fiona’s prawns cost)`
`= 4 xx 6.12`
`= $24.48`
A dog breeder owns 500 dogs.
150 are Ridgebacks and the rest are Pugs.
What is the ratio of Ridgebacks to Pugs?
| `3:5` | `3:7` | `3:9` | `3:10` |
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`3:7`
`text(S)text(ince 150 are ridgebacks,)`
`=> 500-150=350\ text(pugs)`
| `text(Ridgebacks)` | `:\ text(Pugs)` |
| `150` | `: 350` |
| `3` | `: 7` |
Ben spent twice as much money as Mark.
If they spent a total of $90, how much did Ben spend?
| `$15` | `$30` | `$60` | `$180` |
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`$60`
`text(Strategy 1)`
`text(Ratio)`
`text{Ben : Mark = 2 : 1 (3 parts)}`
`text(1 part)\ = $90-:3=$30`
`:.\ text(Ben spent 2 × $30 = $60)`
`text(Strategy 2)`
`text(Let)\ \ $x = text(Amount Mark spent)`
| `2x + x` | `= 90` |
| `x` | `= $30` |
`:.\ text(Ben spent $60.)`
In a tap dancing class, the ratio of boys to girls is 5 : 7.
There are 6 more girls than boys in this group.
How many students are in this group altogether?
| `12` | `13` | `18` | `36` |
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`36`
`5:7\ text(means that given 12 students,)`
`=> 5\ text(boys, 7 girls)`
`text(If 24 students,)`
`=> 10\ text(boys, 14 girls)`
`text(If 36 students,)`
`=> 15\ text(boys, 21 girls)`
`:.\ text(In a class of 36 students, there are 6 extra girls.)`
Sophia and Cailen sold raffle tickets to fund their trip to the National Swimming Titles.
If Cailen had collected $20 more, he would have collected exactly twice as much as Sophia.
Which row of the table shows how much money they could have collected?
| Sophia | Callen | |
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$20 | $40 |
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$25 | $40 |
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$30 | $40 |
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$40 | $70 |
`text(Sophia $30, Callen $40)`
`text(Consider the 3rd option:)`
| `text(Cailen)\ + $20` | `= 2 xx text(Sophia)` |
| `$40 + $20` | `= 2 xx $30` |
| `$60` | `= $60` |
`:.\ text(Sophia $30, Callen $40)`
A design is made using three times as many large beads as small beads.
The mass of each large bead is 140 milligrams.
The mass of each small bead is 40 milligrams.
The total mass of all the beads used is 92 grams.
How many beads are used in total to make the design?
`800`
| `text(Let)\ \ \ x` | `= text( number of small beads)` |
| `3x` | `= text( number of large beads)` |
| `3x (0.14) + x (0.04)` | `= 92` |
| `0.42x + 0.04 x` | `= 92` |
| `0.46 x` | `= 92` |
| `x` | `= 200` |
`:.\ text(There are 200 small beads and)`
`text(600 large beads.)`
`:.\ text(Total beads) = 800`
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?
`4\ text(females)`
`text(Females : Males) = 13 : 11`
`:.\ text(In the room, there are)`
`26\ text(females and 22 males.)`
`:. 4\ text(females need to leave for the)`
`text(ratio to become 1 : 1)`