Question

Me and my sister went shopping. I spent $120 on 3 pairs of jeans and 6 Blouses. my sister spent $90 on 2 pairs of jeans and 5 Blouses. what was the cost of 1 pair of jeans and the cost of 1 blouse? use different methods to solve.

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Answer 1

• jeans: $20
• blouse: $10

Explanation:

You want to solve the following relations for the cost of a pair of jeans and the cost of a blouse.

• 3 jeans + 6 blouses for $120
• 2 jeans + 5 blouses for $90

Matrix method

The equations can be represented by the augmented matrix ...

`\left[\begin{array}c3&6&120\\2&5&90\end{array}\right]`

Reducing this to "reduced row-echelon form" tells you the prices:

• a pair of jeans: $20
• a blouse: $10

Graphing

We can graph the two equations, using x and y for the prices of jeans and a blouse, respectively. The point of intersection of the two lines is ...

(x, y) = (20, 10)

This tells us the prices are ...

• a pair of jeans: $20
• a blouse: $10

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Additional comment

There are algebraic methods of solution as well. In general, we find them more tedious, especially for a system of equations like this where the coefficients are not simple multiples of one another.

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