   Chapter 4.1, Problem 57E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

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$4.00 per piece and the price of pens of Brand Y is $2.80 per piece. Explanation Given Information: The price of pens of Brand X is$4.00 per piece and the price of pens of Brand Y is $2.80 per piece. Elena purchased total number of 12 pens of both types for$42.00.

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 $4.00 and y pens of Brand Y, each pen for$2.80, so, she purchased total pens for 4.00x+2.80y. But Elena purchased all the pens for \$42.00.

Thus,

4.00x+2.80y=42.00

Also, if Elena purchased x pens of Brand X and y pens of Brand Y, then total number of pens she purchased was x+y. But Elena purchased a total 12 of both types.

Thus,

x+y=12

Thus, the two equations are,

4.00x+2.80y=42.00 …… (1)

x+y=12 …… (2)

Consider the equation (1),

Multiply both sides of the equation (1) by 10 to get rid of decimals,

10(4.00x+2.80y)=10(42.00)10(41)x+10(2.81)y=10(421)10(41)x+10(2810)y=10(421)40x+28y=420

Divide both sides of the equation 40x+28y=420 by 4,

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