smc-4608-30-Unitary method ratio

Ratio, SM-Bank 041 MC

An ancient coin is made up of gold and silver in the ratio 1:3.

The coin weighs 21.65 grams.

How many grams of silver are in the ancient coin?

$5.4125$
$7.217$
$14.433$
$16.2375$

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$D$

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$\text{Total parts}=1+3=4$

$\text{Fraction of silver}=\dfrac{3}{4}$

$\text{Silver}=\dfrac{3}{4}\times 21.65=16.2375$

$\Rightarrow D$

Ratio, SM-Bank 038

Damon buys 25 kilograms of salt for his pool for $33.75.

The salt can be purchased in 1 kilogram bags.

How much does 9 kilograms of salt cost? (2 marks)

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$$12.15$

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$\text{C}\text{ost of 1 kilogram}$

$=\dfrac{33.75}{25}$

$= $1.35$

$\therefore\ \text{C}\text{ost of 9 kilograms}$

$= 9\times 1.35$

$= $12.15$

Ratio, SM-Bank 032 MC

Shelley and Carly collect dolls.

The ratio of the number of dolls Shelley 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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$C$

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$\text{Shelley’s dolls represents 3 parts}$

$3\ \text{parts}$	$=12$
$1\ \text{part}$	$=\dfrac{12}{3}=4$

$\text{Carly’s dolls represents 2 parts}$

$=2\times 4=8$

$\therefore\ \text{There Carly owns}\ 8\ \text{dolls.}$

$\Rightarrow C$

Ratio, SM-Bank 031

Jordan has 4 times as many blue pencils as black pencils.

Altogether he has 90 pencils.

How many blue pencils does he have? (2 marks)

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$72\ \text{blue pencils}$

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$\text{Method 1}$

$\text{Ratio of blue to black}=4:1$

$\text{Total parts}=4+1=5$

$\text{Fraction blue}=\dfrac{4}{5}$

$\text{Number of blue pencils}=\dfrac{4}{5}\times 90=72$

$\text{Method 2 (Advanced)}$

$\text{Let}\ \ x = \text{the number of black pencils}$

$\text{Then the number of blue pencils}=4x$

$\text{Total pencils }= x + 4x$	$=5x$
$\rightarrow\ 5x$	$= 90$
$x$	$=\dfrac{90}{5}= 18$

$\therefore \ \text{The number of blue pencils}$

$=90-18= 72$

Ratio, SM-Bank 026

It is known that one of the angles in a triangle is $120^{\circ}$.

Calculate the size of the other 2 angles if they are in the ratio $2:3$. (3 marks)

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$24^{\circ}\ \text{and}\ 36^{\circ}$

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$\text{Angle sum of a triangle}=180^{\circ}$

$\therefore\ \text{Remaining angles}=180-120=60^{\circ}$

$\text{Total parts remaining angles}=2+3=5$

$\text{1st angle}=\dfrac{2}{5}\times 60=24$

$\text{2nd angle}=\dfrac{3}{5}\times 60=36$

$\therefore\ \text{The remaining angles are}\ 24^{\circ}\ \text{and}\ 36^{\circ}.$

Ratio, SM-Bank 024

Joe and Andrew are cleaning fish. For every 4 fish that Joe cleans, Andrew cleans 7.

If Joe cleaned 36 fish, how many did Andrew clean? (2 marks)

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$63 \text{ fish}$

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$\text{Joe’s cleaned fish represents 4 parts}$

$4\ \text{parts}$	$=36$
$1\ \text{part}$	$=\dfrac{36}{4}=9$

$\text{Andrew’s cleaned fish represents 7 parts}$

$=9\times 7=63$

$\therefore\ \text{Andrew cleaned}\ 63\ \text{fish.}$

Ratio, SM-Bank 023

This year there are 108 students in Year 8 and the ratio of Year 7 students to Year 8 students is 8:9.

Use this information to calculate the number of students in Year 7 this year. (2 marks)

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$96 \text{ students in Year 7}$

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$\text{Year 8 represents 9 parts}$

$9\ \text{parts}$	$=108$
$1\ \text{part}$	$=\dfrac{108}{9}=12$

$\text{Year 7 represents 8 parts}$

$=12\times 8=96$

$\therefore\ \text{There are}\ 96\ \text{students in Year 7.}$

\(3\ \text{parts}\)	\(=12\)
\(1\ \text{part}\)	\(=\dfrac{12}{3}=4\)

\(\text{Total pencils }= x + 4x\)	\(=5x\)
\(\rightarrow\ 5x\)	\(= 90\)
\(x\)	\(=\dfrac{90}{5}= 18\)

\(4\ \text{parts}\)	\(=36\)
\(1\ \text{part}\)	\(=\dfrac{36}{4}=9\)

\(9\ \text{parts}\)	\(=108\)
\(1\ \text{part}\)	\(=\dfrac{108}{9}=12\)