Number Patterns
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Writing equations with unknowns II


Two-step problems

We have looked at how to write equations with unknowns, using a problem that only has one part. What if we were to look at a problem involving more than one part? We can still write an equation with unknowns, but we need to remember the order of operations.

In Video 1, we'll look at problems with two different operations in them. We have multiplication and addition, followed by addition and subtraction.



When our problems include division, we are able to think about what we are trying to solve, and what information we already know. By doing this, we can fill in the gaps, and create our equation. In Video 2, we look at a division and addition problem, as well as why brackets can be so important when it comes to the order of operations.


The whole equation!

What if we have no equation at all, and need to start from scratch? That's okay, we can work through the information we know, and think about what we are trying to create. Let's take a look how in our final video.


It's really important to think about the order of operations when you're working with equations.


Worked Examples

Question 1

Rochelle has boxes of pears. Each box contains $19$19 pears, and there are $8$8 pears left over that didn't fit into any of the boxes. In total, she has $160$160 pears.

Let $m$m be the number of boxes of pears that Rochelle has. Fill in the blanks to make an equation in terms of $m$m.

  1. $19\times\editable{}+8=160$19×+8=160

Question 2

Kenneth is a rock climber, and is scaling a cliff face. Part way up he slips, falling $4$4 m down before his harness catches him. He then continues, climbing the remaining $13$13 m to the top of the cliff. The cliff is $23$23 m tall.

Let $a$a be the height at which Kenneth slipped. Fill in the blanks to make an equation.

  1. $a-\editable{}+\editable{}=23$a+=23

Question 3

Xanthe is having dinner with four of her friends, and the $5$5 of them decide to split the cost equally. On the way home, Xanthe also buys a drink for $3$3 pounds. Altogether, she spends $21$21 pounds that evening.

Let $r$r be the total cost of their dinner. Write an equation for the situation using division and addition.

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