Contemporary Mathematics for Busin...

8th Edition

Robert Brechner + 1 other

ISBN: 9781305585447

Textbook Problem

Set up and solve equations for the following business situations.

An online store sells two types of speaker docks for smartphones. The higher-priced speaker dock sells for $190 and the lower-priced speaker dock sells for $80. Last week the store sold three times as many lower-priced speaker docks as higher-priced speaker docks. Combined sales totaled $3,440. How many of each did it sell?

To determine

To calculate: The number of higher-priced speaker dock and lower-priced speaker dock sold last week, if the price of higher-priced speaker dock is $190 and price of lower-priced speaker dock is $80. Last week’s sale of lower-priced speaker is three times as higher-priced and the total sale of last week is $3,440.

Explanation

Given Information:

The price of higher-priced speaker dock is $190 and price of lower-priced speaker dock is $80. Last week’s sale of lower-priced speaker dock is three times as higher-priced speaker dock and the total sale of last week is $3,440.

Formula used:

To solve the equation and prove the solution, follow the steps as mentioned below.

Step 1: Understand the problem and write the facts of the equation.

Step2: List the known and the unknows from the problem.

Step3: Write the equation with the help of following table of key word,

Equal Sign	Addition	Subtraction	Multiplication	Division	Parentheses
Is	And	Less	of	Divide	Times the quantity of
Are	Added to	Less than	Multiply	Divided by	Times the quantity of
Was	Totals	Smaller than	Times	Divided into
Equals	The sum of	Minus	Product of	Quotient of
Gives	Plus	Difference	Multiplied by	Ratio of
Giving	More than	Decreased by	Twice
Leaves	Larger than	Reduced by	Double
Results in	Increased by	Take away	Triple
Produces	Greater than	Loss of	At
yields	exceeds	Fewer than	@

Step4: Solve the equation by rearrange the unknown values to the left side and known values to the right side of the equal sign.

Step5: Prove the solution by substituting the value obtained from step 4 in the equation formed in step 4 then check the left and right of the equation if, they are equal then the answer is correct.

Calculation:

Underline the keyword by using the table of of key word.

The sum of price of each item multiply by its quantity equals total price, $3,440.

Suppose that number of higher-priced speaker sold is X.

Consider the number of lower-priced speaker is three times as higher-priced, 3X.

Consider the price of higher-priced speaker dock, $190 and the price of lower-priced speaker dock, $80.

So, the total sale of higher-priced speaker is $190X and of lowered-priced speaker is $80(3X)

Also consider the total sale, $190X+$80(3X)=$3,440

Now solve the equation 190X+80(3X)=3,440

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