Ratios, Rates and Best Buys - Questions - Class Mathematics School Portal

Ratios, Rates and Best Buys - Questions

Question 1

37772

Simplify the ratio $21:28:42$

Answer

$3:4:6$

Worked Solution

Question 2

15428

Simplify the following ratio.

$500~\text{g}$ : $2.2~\text{kg}$

Answer

$5:22$

Worked Solution

Question 3

41578

Father divided the money among Max , Evie and Zoe in the ratio $2 : 3 : 5$. If Zoe received $180, find the total amount and the money received by Max.

Answer

$\$72$

Worked Solution

\begin{align} \text{Money received by Max} &\text{, Evie and Zoe are in ratio }2:3:5\\
\text{Total parts}& =10\\
\text{Money received by Max }&=2x,\text{ Evie }=3x \text{ and Zoe}=5x
\end{align}
\begin{align*} 5x&=180 \\
x&=36\\
\text{Total amount}&=36 \times 10\\
&=$360
\end{align*}\begin{align*} \text{Money received by Max}&=2x \\ &=2 \times 36 \\ &=72 \end{align*}

Question 4

41577

Simplify $4~\text{kg} : 400~\text{g}$

Answer

$10:1$

Worked Solution

Question 5

15420

In a cricket match between India and Australia, Australia scored 280 runs in 50 overs while India made 281 runs in 45 overs.

a) What is the run rate of Australia?
b) What is the run rate of India?

Answer

$a)~\text{5.6 runs/over}$

$b)~\text{6.24 runs/over}$

Worked Solution

Question 6

15463

Which of the following is a better buy

A pack of ${\rm{9}}$ toilet rolls costs ${\rm{\$ 4}}{\rm{.23}}$

A pack of ${\rm{4}}$ toilet rolls costs ${\rm{\$ 1}}{\rm{.96}}$

Answer

$9~\rm{ pack}$

Worked Solution

Question 7

41579

Henry and Isla won $90000 in a lottery. If they share the prize in the ratio $36 : 54$, how much does Henry receive?

Answer

$\$36000$

Worked Solution

\begin{align*} \text{Total number of parts} &=36+54 \\ &=90 \end{align*} $\begin{aligned} \therefore \quad &90 \text{ parts}=90000 \\ &1 \text{ part}=1000 \end{aligned}$ \begin{align*} \text{Henry's share}&=36 \times 1000 \\ &=\$36000 \end{align*}

Question 8

41580

A car maintains an average speed of 80 km/h. Calculate how far it will travel:

a. In 3 hours
b. From 3 pm to 8 pm

Answer

a) $240~\text{km}$ b) $400~\text{km}$

Worked Solution

Question 9

41581

Isabella earns $320 for an 9-hour day.

a. Express this pay as an hourly rate ($/h).
b. How much would she earn in a 50-hour week?
c. How many hours will it take her to earn $2100? Write the answer correct to 1 decimal place.

Answer

a) $35.56 / hour b) $1778 c) 59.1 hours

Worked Solution

Question 10

15464

Potatoes cost ${\rm{\$ 18}}{\rm{.75}}$ for a ${\rm{12}}{\rm{.5 ~kg}}$ bag at a farm shop.The same type of potatoes cost ${\rm{\$ 4}}{\rm{.50}}$ for a ${\rm{ 2}}{\rm{.5 ~kg}}$ bag at a supermarket. Where are the potatoes the better value?

Answer

${\rm{farm ~shop}}$

Worked Solution

Question 11

115196

Determine the best buy $15 \mathrm{~g}$ for $\$ 4.95$ on $25 \mathrm{~g}$ for $\$ 9.50$

Answer

$15 \mathrm{~g}$

Worked Solution

Question 12

115129

The ratio of a fathers age to the age of his daughter is $11: 3$. If the father age is 44, find the age of the daughter.

Answer

Worked Solution

Question 13

115130

James' heart beats at 62 beats / min. How many times will it beat in 1 hour?

Answer

3720

Worked Solution

Question 14

115132

Birth rates are given as births $/ 1000$ people. A city's birth rate is 14 births per 1000 people. If there were 560 births in the city last year, what is the population?

Answer

40000

Worked Solution

Question 15

115199

Determine the best buy: $200 \mathrm{~mL}$ for $\$ 8.50$ or $500 \mathrm{ml}$ for $\$ 20.80$.

Answer

$500 \mathrm{~mL}$

Worked Solution

Question 16

115200

Bird seed is sold in 3 sizes; $500 \mathrm{~g}$ for $\$ 1.80$, $1 \mathrm{~kg}$ for $\$ 3.40$ and $1.75 \mathrm{~kg}$ for $\$ 5.80$. Which size represents the better value?

Answer

$1.75\mathrm{~kg}$

Worked Solution