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Equations, SM-Bank 015

A square with side length  \(\large x\)  has an area of \(81\ \text{cm}^2\).

Write an equation and solve it to find the side length.  (2 marks)

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\(x^2=81\  \ ,\  \  x=9\ \text{cm}\)

Show Worked Solution
\(x^2\) \(=81\)
\(x\) \(=\sqrt{81}\)
\(x\) \(=9\)

 
\(\therefore\ \text{The side length is }9\ \text{cm}\)

Equations, SM-Bank 014

A number  \(\large p\)  is halved and the result is 125.6.

Write an equation and solve it to find the number.  (2 marks)

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\(\dfrac{p}{2}=125.6\  \ ,\  \  p=251.2\)

Show Worked Solution
\(\dfrac{p}{2}\) \(=125.6\)
\(p\) \(=2\times 125.6\)
\(p\) \(=251.2\)

 
\(\therefore\ \text{The number is }251.2\)

Equations, SM-Bank 013

A number  \(\large w\)  is tripled and the result is 141.

Write an equation and solve it to find the number.  (2 marks)

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\(3w=141\  \ ,\  \  w=47\)

Show Worked Solution
\(3w\) \(=141\)
\(w\) \(=\dfrac{141}{3}\)
\(w\) \(=47\)

 
\(\therefore\ \text{The number is }47\)

Equations, SM-Bank 012

Verity and three of her friends won  \(x\) dollars in a lottery. When the money was divided evenly between the four friends they each received \($124\ 500\).

Write an equation and solve it to find out the total amount of their lottery winnings.  (2 marks)

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\(\dfrac{x}{4}=124\ 500\  \ ,\  \  x=$498\ 000\)

Show Worked Solution
\(\dfrac{x}{4}\) \(=124\ 500\)
\(x\) \(=4\times 124\ 500\)
\(x\) \(=498\ 000\)

 
\(\therefore\ \text{The amount of their total winnings was}\ $498\ 000\)

Equations, SM-Bank 011

Josh is currently \(x\) years old. In \(15\) years he will be 42.

Write an equation and solve it to find Josh's current age.  (2 marks)

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\(x+15=42\  \ ,\  \  x=27\ \text{years old}\)

Show Worked Solution
\(x+15\) \(=42\)
\(x\) \(=42-15\)
\(x\) \(=27\)

 
\(\therefore\ \text{Josh’s current age is}\ 27\ \text{years}\)

Equations, SM-Bank 010

Preston is paid \(x\) dollars per basket of grapes he picks. Yesterday he picked \(8\) baskets and he earned $306.

Write an equation and solve it to find Preston's rate of pay per basket.  (2 marks)

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\(8x=306\  \ ,\  \  x=$38.25\)

Show Worked Solution
\(8x\) \(=306\)
\(x\) \(=\dfrac{306}{8}\)
\(x\) \(=38.25\)

 
\(\therefore\ \text{Preston’s rate of pay per basket is}\ $38.25\)

Equations, SM-Bank 009

Missy is paid \(x\) dollars per hour. Last week she worked \(20\) hours and she earned $350.

Write an equation and solve it to find Missy's hourly rate of pay.  (2 marks)

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\(20x=350\  \ ,\  \  x=$17.50\)

Show Worked Solution
\(20x\) \(=350\)
\(x\) \(=\dfrac{350}{20}\)
\(x\) \(=17.50\)

 
\(\therefore\ \text{Missy’s hourly rate of pay is}\ $17.50\)

Equations, SM-Bank 008

Solve the following one-step equations.

  1. \(s-3=-4\)  (1 mark)

  2. \(c+4=-2\)  (1 mark)

  3. \(-3x=36\)  (1 mark)

  4. \(\dfrac{b}{6}=-4\)  (1 mark)

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a.    \(s=-1\)

b.    \(c=-6\)

c.    \(x=-12\)

d.    \(b=-24\)

Show Worked Solution
a.    \(s-3\) \(=-4\)
  \(s\) \(=-4+3\)
  \(s\) \(=-1\)

 

b.    \(c+4\) \(=-2\)
  \(c\) \(=-2-4\)
  \(c\) \(=-6\)

 

c.    \(-3x\) \(=36\)
  \(x\) \(=\dfrac{36}{-3}\)
  \(x\) \(=-12\)

 

d.    \(\dfrac{b}{6}\) \(=-4\)
  \(b\) \(=-4\times 6\)
  \(b\) \(=-24\)

Equations, SM-Bank 007

Solve the following one-step equations.

  1. \(x+4=10\)  (1 mark)

  2. \(m-7=2\)  (1 mark)

  3. \(2u=28\)  (1 mark)

  4. \(\dfrac{r}{2}=5\)  (1 mark)

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a.    \(x=6\)

b.    \(m=9\)

c.    \(u=14\)

d.    \(r=10\)

Show Worked Solution
a.    \(x+4\) \(=10\)
  \(x\) \(=10-4\)
  \(x\) \(=6\)

 

b.    \(m-7\) \(=2\)
  \(m\) \(=2+7\)
  \(m\) \(=9\)

 

c.    \(2u\) \(=28\)
  \(u\) \(=\dfrac{28}{2}\)
  \(u\) \(=14\)

 

d.    \(\dfrac{r}{2}\) \(=5\)
  \(r\) \(=5\times 2\)
  \(r\) \(=10\)