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.