Once we have translated a verbal situation into an ** equation **, we can use the equation to solve the problem by finding the unkown value of the** variable **.

When working to solve problems, always be sure to:

- Read the question at least twice and find keywords.
- Be clear what your variable is representing, for example instead of saying that "x is chickens" we could say "x is the number of chickens" or "x is the weight of each chicken."
- Check your answer to see if it is reasonable and then check it by substituting into your equation.

Let's consider the following scenario:

You bought a chocolate bar and two bags of chips. The price of the chocolate bar was clearly marked as \$3 but there was no price on the chips. You spent a total of \$7. How much did each bag of chips cost?

The unknown value in this scenario is the cost of one bag of chips. We can represent this scenario and calculate the cost of the chips using a pictorial model like this:

We can also translate the scenario into an equation. The cost of the bag of chips is unknown, so we will use c to represent this. This scenario can be translated into the equation 2c+3=7. Now that the scenario is translated, we can solve the equation.

\displaystyle 2c+3 | \displaystyle = | \displaystyle 7 | Translate the equation |

\displaystyle 2c | \displaystyle = | \displaystyle 4 | Subtract 4 from both sides |

\displaystyle c | \displaystyle = | \displaystyle 2 | Divide both sides by 2 |

Each bag of chips costs \$2.

We can verify our ** solution ** by substiuting 2 into the equation for c.

\displaystyle 2(2)+3 | \displaystyle = | \displaystyle 7 | Substitute c=2 |

\displaystyle 4+3 | \displaystyle = | \displaystyle 7 | Evaluate the multiplication |

\displaystyle 7 | \displaystyle = | \displaystyle 7 | Evaluate the addition |

c = 2 is a solution to the equation 2c + 3 = 7 because 2(2) + 3 = 7.

The solution of c=2 means that each bag of chips costs \$2. Given the context, this answer makes sense.

The sum of 7 and 8x is equal to 47.

Construct the equation and find the value of x.

Worked Solution

Sally and Eileen do some fundraising for their sporting team. Together, they raised \$ 600. If Sally raised \$272 more than Eileen, and Eileen raised \$ p:

a

Write and solve an equation in terms of p that represents the relationship between the different amounts.

Worked Solution

b

Now, calculate how much Sally raised.

Worked Solution

Consider the following equation.

7.50h+25=115

a

Create a real world scenario that could be represented by the equation.

Worked Solution

b

Solve the equation and explain the answer in context to the scenario you created in part a.

Worked Solution

Idea summary

When working to solve problems, always be sure to:

- Read the question at least twice and find keywords.
- Be clear what your variable is representing, for example instead of saying that "x is chickens" we could say "x is the number of chickens" or "x is the weight of each chicken."
- Check your answer to see if it is reasonable and then check it by substituting into your equation.