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# Tag Archives: Primary

## Let’s Learn Mathematics (Primary Level) 3

Disclaimer: This Mathematics question is purely created for discussion purpose. Any resemblance to actual questions from books or schools is coincidental.

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We have discussed about simple algebra in Let’s Learn Mathematics (Primary Level). Though algebra is formally introduced in secondary schools, the model method is taught in primary schools as an introduction to algebra. Thus, you can see the importance of learning algebra.

The question of this post is considered advanced for primary students, nonetheless it is for primary students. Take your time to understand the question and the solution; they are helpful in learning algebra up to secondary schools.

Q: 3 shirts and a pair of trousers cost $63.50. A shirt and 2 pairs of trousers cost $27. Find the cost of a shirt.

A: First you need to draw the diagram to show the relationship of the equations, based on the question. The first sentence (3 shirts and a pair of trousers cost $63.50) forms an equation and the second equation forms another equation. [Please refer to The Almighty Algebra for notes.]

In the above diagram, the blue rectangle represents the shirt and the yellow triangle represents the pair of trousers.

If the student has been solving similar questions, he / she will start by adding or subtracting the two equations.

s = a shirt, t = a pair of trousers

Equation 1, 3s + t = 63.50

Equation 2, s + 2t = 27

Adding equation 1 and equation 2, 4s + 3t = 90.50

Subtracting equation 2 from equation 1, 2s − t = 36.50

This is where students may face the problem to continue solving the problem. They have all the equations but the equations are leading them to nowhere. No matter it is adding or subtracting, you end up with more equations with no solution.

You can apply any Mathematics operation to any equation.

The Mathematics operation includes adding, subtracting, multiplying and dividing. Yes, many students have not thought of multiplying the equations. Nonetheless, we do not encourage students to divide the equations because it will lead to decimals or fractions. It is difficult to solve the question, it is more difficult to solve the question with decimals or fractions.

Back to the question, the question is only asking for the cost of a shirt. So, to simplify the question, we must “eliminate” the cost of a pair of trousers.

Equation 1, 3s + t = 63.50

Equation 2, s + 2t = 27

The fastest way to get rid of “t” is to multiply 2 to equation 1 and then subtract equation 2 from the new equation (equation 3).

Equation 1 x2, 6s + 2t = 127 (Equation 3)

Equation 3 − Equation 2, 5s = 100 [There is no more “t” because 2t − 2t = 0]

s = 100 ÷ 5

s = 20

The cost of a shirt is $20.

## Let’s Learn Mathematics (Primary Level) 2

Disclaimer: This Mathematics question is purely created for discussion purpose. Any resemblance to actual questions from books or schools is coincidental.

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Q: In a seminar, the ratio of the number of men to the number of women was 2:3. On the following day, two more men attended the seminar. The ratio became 5:6. How many participants were there in the seminar at first?

Understanding the question

This is a question about ratio. The ratio has changed because the number of men has changed. Thus, steps to solve this question are:

1. Make the ratio with the same number of women on the first and second day of the seminar. It is because the number of women is unchanged.

2. Find out the change (difference) of the number of men on the first and second day of the seminar.

3. The difference of the number of men on the first and second day is 2, which is also equivalent to the answer from step 2.

4. Find the number of participants on the first day.

Step-by-step Answer

1. The men-women ratio on the first day => 2:3 = 4:6

The men-women ratio on the second day => 5:6

2. Comparing the men-women ratio on the first and second day => 4:6 and 5:6

The difference of the number of men on the first and second day = 5 – 4 = 1

3. 1 unit of difference = 2 more men attended the seminar on the second day.

4. Total units on the first day = 4 + 6 = 10

Total participants on the first day = 10 x 2

= 20 participants

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Checking the answer

On the first day, there were 20 participants with the ratio 2:3. Thus, the number of men on the first day was (20 x 2) ÷ 5 = 8.

On the second day, two more men attended the seminar. Thus, the number of men on the second day was 2 + 8 = 10.

The number of women on the first and second day was = 20 – 8 = 12.

The men-women ratio on the second day = 10:12

= 5:6

Thus, the answer, 20 participants, is correct.

Note to parents: If your child encounters difficult questions, asks him / her to check the answer. Checking the answer is a good way to reassure your child that he / she has answered the question correctly.