Chapter 4.1, Problem 57E

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7th Edition

Stefan Waner + 1 other

ISBN: 9781337274203

Textbook Problem

**Purchasing** (*from the GMAT*) Elena purchased Brand *X* pens for $4.00 apiece and Brand *Y* pens for $2.80 apiece. If Elena purchased a total of 12 of these pens for $42.00, how many Brand *X* pens did she purchase?

To determine

**To calculate:** The number of pens of Brand X purchased by Elena, if the price of pens of Brand X is

Explanation

**Given Information:**

The price of pens of Brand X is

**Formula used:**

Elimination method:

Step 1: Consider the linear equations in two variables.

Step 2: The equations are multiplied with suitable non-zero numbers to convert the coefficients to equals of opposite signs.

Step 3: The equations are combined to eliminate one variable, and the value of the other variable is calculated.

Step 4: Substitute the value of the calculated variable into one of the equations and calculate the value of the other variable.

**Calculation:**

Consider the problem,

Let *x* be the number of pens of Brand X purchased and *y* be the number of pens of Brand Y purchased.

Here, if Elena purchased *x* pens of Brand X, each pen for *y* pens of Brand Y, each pen for

Thus,

Also, if Elena purchased *x* pens of Brand X and *y* pens of Brand Y, then total number of pens she purchased was

Thus,

Thus, the two equations are,

Consider the equation (1),

Multiply both sides of the equation (1) by

Divide both sides of the equation

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