Category: Problem Solving and Proofs

Solving Word Problems in Numbers using Algebra Part 3

High School Algebra, Problem Solving and Proofs

This is the last part of the Solving Number Problems Series. In this post, we are going to solve number problems in disguise, or numbers problems with different contexts. The previous two parts in this series you may want to read are Solving Word Problems in Numbers using Algebra are Part 1 and Part 2.

Example 7

Jack is twice as old as Rose. Two years from now, the sum of their ages is 40. How old are they now?

Solution

This problem is an age problem but it is very similar to number problems.  As stated, there are two points in time: now and 2 years from now.

Now, Jack is twice as old as Rose. That means that if Rose is 15, then Jack is 30. That means that if the age of Jack is 2x, then Rose’s age is x. Therefore, we have the following representation.  » Read more

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Angle Sum of Polygons in Tessellated Triangles

High School Geometry, High School Mathematics, Problem Solving and Proofs

Tessellated triangles are not only beautiful but that they are also interesting. Tessellating them will prove the angle sum of polygons particularly parallelogram, trapezoid, and hexagon. The term angle sum means the sum of the interior angles.

Let us start with the knowledge that the angle sum of a triangle is 180 degrees. Copying a triangle with angle measures x, y, and z, and rotating it 180 degrees will give us the first two figures. The tessellated copies are shown in the next figure.

tessellated triangle

Using the three figures above, we can prove the following.  » Read more

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Solving Math Word Problems in Numbers Using Algebra

High School Algebra, High School Mathematics, Problem Solving and Proofs

This is the third part of the Solving Math Word Problem Solving Series on Numbers for Grade 6 – 8 students. The first part was on solving number problems mentally by working backward. The second part discussed on solving number problems using the model method. In this post, we are going to discuss how to solve word problems using Algebra if the mental and model methods fail. We will start with simple problems and will continue to solve more complicated problems later. We will use the problems we discussed in the first two parts of this series. Note that the discussion in this post is quite detailed because it is designed for beginners particularly middle school and high school students.

Example 1 One number is 1 more than the other. Their sum is 47. What are the numbers?

Solution

First Sentence: One number is 1 more than the other.

If there are two numbers and the other one is 1 bigger than the number, then if the smaller number is 5, the other is 5 + 1 or 6. So, since we don’t know what the number is, we let the number n. This means that the larger number is n + 1.  » Read more

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