Aussie Maths & Science Teachers: Save your time with SmarterEd
Lucia is saving her money to buy a jet ski.
After 3 months, she had saved 40% of the cost of the jet ski.
After 5 months, she had saved another $1200 and now had 60% of the cost of the jet ski.
How much does the jet ski cost? (2 marks)
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\($6000\)
| \(60\%-40\%\) | \(= $1200\) |
| \(\therefore 20\%\) | \(= $1200\) |
| \(\therefore\ 1\%\) | \(= $60\) |
| \(\therefore\ \text{The cost of the jet ski}\) | \(= 100\times 60= $6000\) |
Lancelot bought a new round table for $2810.50 inclusive of 10% GST.
What was the price of the round table before the GST was added? (2 marks)
\($2555\)
\(\text{Round table has had 10% added to the price.}\)
\(\therefore\ $2810.50\ \text{represents}\ 110\text{%}\ \text{of the original price}\)
| \(\therefore\ \dfrac{110}{100}\ \times\ \text{Original price}\) | \(=$2810.50\) |
| \(\therefore\ \text{Original price}\) | \(=\dfrac{$2810.50\times 10}{11}\) |
| \(=$2555\) |
Mickey bought a plane ticket to London for $1716 inclusive of 10% GST.
What was the price of the ticket before the GST was added? (2 marks)
\($1560\)
\(\text{Plane ticket has had 10% added to the price.}\)
\(\therefore\ $1716\ \text{represents}\ 110\text{%}\ \text{of the original price}\)
| \(\therefore\ \dfrac{110}{100}\ \times\ \text{Original price}\) | \(=$1716\) |
| \(\therefore\ \text{Original price}\) | \(=\dfrac{$1716\times 10}{11}\) |
| \(=$1560\) |
James purchased a pair of football boots for $358.05.
This price included 10% GST.
What was the price of the shoes before the GST was added? (2 marks)
\($325.50\)
\(\text{Football boots have had 10% added to the price.}\)
\(\therefore\ $358.05\ \text{represents}\ 110\text{%}\ \text{of the original price}\)
| \(\therefore\ \dfrac{110}{100}\ \times\ \text{Original price}\) | \(=$358.05\) |
| \(\therefore\ \text{Original price}\) | \(=\dfrac{358.05\times 10}{11}\) |
| \(=$325.50\) |
Minerva purchased a book online and a discount of 35% was applied at checkout.
If Minerva paid $29.90 with the discount, what was the original price of the book. (2 marks)
\($46\)
\(\text{Book price discounted by 35%.}\)
\(\therefore\ $29.90\ \text{represents}\ \dfrac{65}{100}\ \text{of the original price}\)
| \(\therefore\ \dfrac{65}{100}\ \times\ \text{Original price}\) | \(=$29.90\) |
| \(\therefore\ \text{Original price}\) | \(=\dfrac{29.90\times 100}{65}=$46\) |
Fred owns a property which is currently experiencing a drought.
Fred's dam is currently 30% below its maximum capacity.
Calculate the capacity of the dam when full if it currently holds \(280\ 000\) litres? (2 marks)
\(400\ 000\ \text{litres}\)
\(\text{Capacity has decreased by 30%.}\)
\(\therefore\ 280\ 000\ \text{litres represents}\ \dfrac{70}{100}\ \text{of the full capacity}\)
| \(\therefore\ \dfrac{7}{10}\ \times\ \text{Full capacity}\) | \(=280\ 000\) |
| \(\therefore\ \text{Full capacity}\) | \(=\dfrac{280\ 000\times 10}{7}=400\ 000\ \text{litres}\) |
Asti bought a formal dress that was on sale at a 75% discount.
Calculate the original price of the formal dress if the sale price was $60? (2 marks)
\($240\)
\(\text{Dress has been discounted by 75%.}\)
\(\therefore\ $60\ \text{represents}\ \dfrac{1}{4}\ \text{of the original price.}\)
| \(\therefore\ \dfrac{1}{4}\ \times\ \text{Original Price}\) | \(=60\) |
| \(\therefore\ \text{Original Price}\) | \(=60\times 4=$240\) |
Richard bought a second hand snowboard at a cost of $390.
Richard had to spend 65% of his savings to buy the snowboard.
How much did Richard have in his savings after buying the snowboard? (2 marks)
\($210\)
| \(65\text{%}\times \text{Savings}\) | \(= $390\) |
| \(\therefore\ \text{Savings}\) | \(=\dfrac{390}{0.65}= $600\) |
| \(\therefore\ \text{Savings left}\) | \(= 600-390= $210\) |
Harrison was saving his money to buy a cricket bat.
After 1 month, he had saved 45% of the bat's cost.
After 2 months, he had saved another $90 and now had 75% of the bat's cost.
How much does the bat cost? (2 marks)
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\($300\)
| \(75\%-45\%\) | \(= $90\) |
| \(30\%\) | \(= $90\) |
| \(\therefore\ 1\%\) | \(= $3\) |
| \(\therefore\ \text{The bat cost}\) | \(= 100\times 3= $300\) |