Algebra method
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This document explains how to solve a word problem about the number of keychains Susan, Amy, and Mary have using algebra. It introduces letting Y represent Susan's keychains, writes an equation for the total keychains as 22Y + 34, solves to find Y = 6, and uses that value to determine each person's keychains. The conclusion compares this algebraic method to modeling and explains algebra is more efficient and better for harder problems.
Algebra method
- 1. Algebra method In this question, we only need to use one symbol to represent a value.
- 2. Solving So, Let Y be the number of keychains Susan has. Total number of keychains they have would be Y(Susan)+20Y(Amy) + Y+34(Mary), which gives us 22Y + 34.
- 3. Solving Since the number of keychains they have altogether is 166, 22Y+34=166 22Y=166-34 22Y=132 Y=6
- 4. Solving Now, we simply use the value of Y to find out how many keychains each of them have. Amy has 20Y keychains, so Amy has 20 x Y= 120 keychains Susan has Y keychains, so Susan has 6 keychains Mary has Y+34 keychains, so Mary has 6+34=40 keychains
- 5. Conclusion As you can see, this method is much faster than the modelling method This is because you don’t have to spend time to slowly draw out the units
- 6. Conclusion Also, the modelling method and Algebra method do have some similarities, but the Algebra method is more efficient Algebra is also better for solving tougher problems as compared to modelling (not very obvious in this example as the question was fairly simple)