smc-3147-25-% increase/decrease

Number, NAP-L3-NC03

Santana is buying a guitar string.

Some of the strings are on sale.

Select the string that will be cheapest.

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`text(Sale: take 20% off)`

Show Worked Solution

`text(C)text(ost of each option:)`

`$17`

`$35\ text(less 50%) = $17.50`

`text($20 less 20%) = 20 – 4 = $16`

`text($24 less 25%) = 24 – 6 = $18`

`:.\ text(Sale: take 20% off is the cheapest string.)`

Number, NAP-K3-NC08 SA

Michael purchases a 3D printer worth $2 490 000.

He was given a 10% discount.

What was the price paid by Michael after the discount?

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`$2\ 241\ 000`

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`text(Discount)`	`= 10text(%) xx 2\ 490\ 000`
	`= 249\ 000`

`:.\ text(Price)`	`= 2\ 490\ 000 – 249\ 000`
	`= $2\ 241\ 000`

Number, NAP-A3-CA24

A hockey stick is on sale, reduced from $220 to $165.

What percentage discount has been applied?

`text(25%)`	`text(33%)`	`text(45%)`	`text(55%)`

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`text(25%)`

Show Worked Solution

`text(Discount)`	`= text(reduction)/text(original price) xx 100`
	`= ((220 – 165))/220 xx 100`
	`= 25text(%)`

Number, NAP-A4-CA14

The population of Australian states in 2015 and 2016 is recorded in the table below.

Some data for Western Australia is not shown.

What was the population of Western Australia (WA) close to in 2016?

`2\ 773\ 100`	`2\ 710\ 500`	`2\ 147\ 600`	`2\ 091\ 300`

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`2\ 091\ 300`

Show Worked Solution

`text(WA Population in 2016)`

`= 2\ 085\ 021 xx 1.003`

`~~ 2\ 091\ 300`

Number, NAP-J3-CA30 SA

Don buys a cricket ball, originally marked $30, that is discounted by 25%.

He also has a loyalty card that gives him another 20% off the sale price.

What is the final cost of the ball?

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`$18`

Show Worked Solution

`text(Solution 1)`

`text(Sale price)`	`= 30 – (25text(%) xx 30)`
	`=30 – 7.50`
	`= $22.50`

`:.\ text(Final cost)`	`= 22.50 – (20text(%) xx 22.50)`
	`= $18`

`text{Solution 2 (advanced)}`

`text(Final cost)`	`= 30 xx 0.75 xx 0.8 `
	`= $18`

Number, NAP-B3-CA18

Jake bought a mobile phone at 25% off the original price.

The original price was $380.

How much did Jake pay for the mobile phone?

`$95`	`$285`	`$342`	`$355`

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`$285`

Show Worked Solution

`text(Price of mobile)`	`=380 – (text(25%) xx 380)`
	`=380 – 95`
	`=$285`

Number, NAP-C3-CA30 SA

A sport store has a sale.

What is the difference in the sale prices of these two tents?

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`$7.50`

Show Worked Solution

`text(Price of tent 1)`	`= 85 – 30text(%) xx 85 `
	`= 85 – 25.5`
	`= $59.50`
`text(Price of tent 2)`	`= 80 – 35text(%) xx 80`
	`= 80 – 28.0`
	`= $52.00`

`:.\ text(Price difference)`	`= 59.5 – 52`
	`= $7.50`

Number, NAP-G3-CA28 SA

Walker is doing an intensive swim program over the summer holidays.

In his first session, he swims 50 laps.

In his second session, he swims 30% more laps than his first session.

In his third session, he swims 20% more laps than his second session.

How many laps does he swim at his third practice?

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`78\ text(laps)`

Show Worked Solution

`text(1st session) = 50\ text(laps)`

`text(2nd session)`	`= 50 + (30text(%) xx 50)`
	`= 50 + 15`
	`= 65\ text(laps)`

`text(3rd session)`	`= 65 + (20text(%) xx 65)`
	`= 65 + 13`
	`= 78\ text(laps)`

Number, NAP-H3-NC14

Ricky wants to buy a cricket bat that has a normal price of $160.

He is given a 10% discount.

What is the value of the discount?

`$1.60`	`$10`	`$16`	`$150`

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`$16`

Show Worked Solution

`text(Value of the discount)`

`= 10 text(%) xx 160`

`=$16`

Number, NAP-I3-CA23

The table below lists the original price and the amount of discount of a pair of jeans at four different shops.

Which shop has the lowest sale price for the jeans?

`text(A)`	`text(B)`	`text(C)`	`text(D)`

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`text(Shop B)`

Show Worked Solution

`text(Consider the sale price at each shop:)`

`text(A)`	`= 20 – (25text{%} xx 20) = $15`
`text(B)`	`= 21 – (1/3 xx 21) = $14`
`text(C)`	`= 18 – (20 text{%} xx 18) = $14.40`
`text(D)`	`= 17 – 2 = $15`

`:.\ text(Shop B has the lowest sale price.)`

Number, NAP-I3-NC27 SA

A box of golf balls normally cost $19.50.

During a sale, the golf shop took 10% off the regular price of the balls.

What is the new sale price of the golf balls?

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`$17.55`

Show Worked Solution

`text(10% discount)`	`= 19.50/10`
	`= $1.95`

`:.\ text(Sale price)`	`= $19.50 – $1.95`
	`= $17.55`

Number, NAP-G4-CA18

Marty and Paul swam 3 km in an ocean swimming race.

Marty finished in a time of 1 hour and 10 minutes.

Paul took 25% longer than Marty.

Approximately how long did Paul take to finish the race?

`88\ text(minutes)`	`95\ text(minutes)`	`135\ text(minutes)`	`138\ text(minutes)`

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`88\ text(minutes)`

Show Worked Solution

`text(Paul’s time)`

`= (1\ text{hour and 10 minutes)} xx text(125%)`

`= 70 xx text(125%)`

`= 87.5\ text(minutes)`

`:.\ text(88 minutes is the closest choice.)`