Pre-Algebra

What is the price at the question mark?

Starting With Variables

           

The symbols above are direct references to what they mean, but we can use any symbols we like. If CC is the cost of a cup of cocoa and II is the cost of one cone of ice cream, the first two lines above are equivalent to

C+C+I+I+I=19I+I=6\begin{aligned} C + C + I + I + I &= 19 \\ I + I &= 6 \end{aligned}

CC and II here are both variables, values that can vary and are only fixed to set numbers in order to fulfill the specific conditions of the problem.

Starting With Variables

           

Micah has $20.\$20. Sara has $4.\$4. If Micah gives some money to Sara, how much does Micah need to give so at the end they both have the same amount of money?

Starting With Variables

           

The prior problem could be represented with the variable aa being the amount of money given:

  • Micah starts with 2020 and loses a,a, so she has 20a 20 - a at the end
  • Sara starts with 44 and gains a,a, so she has 4+a 4 + a at the end

In other words, the problem was to find aa such that

20a=4+a 20 - a = 4 + a

Starting With Variables

           

Three squares each contain an identical number of dots.

How many dots should go in each square so that the squares have a combined total of 2121 dots?

Starting With Variables

           

The count of dots per square is acting as a variable. Not only is it an amount that can vary but it can also be reused, and each instance of the variable represents the same number of dots.

With letters, we could assign the number of dots as D,D, and the previous question is asking when

D+D+D D + D + D

equals 21.21.

We can also simplify D+D+D D + D + D into 3×D, 3 \times D , which is considered equivalent.

Starting With Variables

           
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