A table is useful to organize information and recognize relationships.
Practice makes perfect
A table is useful to organize information and recognize relationships. Let's see an example.
Example
Janice, Tia, and Amy collect marbles. Janice has twice as marbles as Tia. Amy has three more marbles than Tia. Next week they will buy three marbles each. The number of marbles Janice will have is the same as the number of marbles Amy will have. Find the number of marbles each of the girls has.
Using a table
Let's start by writing an expression for the number of marbles they have. Let x be the number of marbles Tia has.
Verbal Phrase
Algebraic Expression
Janice
Twice as Tia
2 x
Tia
-
x
Amy
Three more than Tia
3 + x
Considering they will have three more marbles each, construct a table to organize the information.
Number of Marbles They Currently Have
Number of Marbles They Will Have Next Week
Janice
2x
2x + 3
Tia
x
x + 3
Amy
3+x
3+x + 3
Now we have expressions for the number of marbles the three girls will have next week.
Setting and solving an equation
The number of marbles Janice will have is the same as the number of marbles Amy will have.
2x+3=3+x+3
We will sove the above equation to find the value of x. Let's start by simplifying the right-hand side.
In the context of the problem, x is the number of marbles Tia has. Thus, she has 3 marbles. Since Janice has twice as marbles as Tia, she has 6 marbles. Since Amy has three more than Tia, she also has 6 marbles.
Tia:& 3marbles
Janice:& 6marbles
Amy:& 6marbles
