Problem solving with Equations

Sometimes we will come across questions that ask us to find an unknown, but the information they give us is not enough to immediately make the solution obvious. 

It is up to us to put the pieces together to construct an equation which will make it easier to solve the problem and find the unknown. 

The key is to find out what information is important. We can do this by looking for terms such as sum, minus, or equals and most importantly, by finding out what the question is asking us to solve.

Let's have a look at some problems that can be more easily solved by forming an equation.

 

Examples

Question 1

Solve: The product of $5$5 with the sum of $x$x and $7$7 equals to $50$50. Construct an equation and find the value of $x$x.

 

Question 2

Solve: The product of $5$5 with the difference of $5$5 from $x$x equals to $-15$−15. Construct an equation and find the value of $x$x.

Question 3

Solve: The sum of $7$7 and $8x$8x equals to $47$47. Construct an equation and find the value of $x$x.

 

Question 4

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

a) Write an equation in terms of $p$p that represents the relationship between the different amounts, and solve for $p$p.

 

b) Calculate how much Sally raised.