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Problem of the Week Answers

Problem of the Week Answer

Week #1

Bob’s yearly salary is $30,000, and it will be increased by $3,000 a year.
Jake’s yearly salary is $20,000, and it will be increased by $5,000 a year.
In how many years will both Bob and Jake have the same yearly salary?
 

ANSWER: 5 years

Solution #1:  Create a chart showing their salaries each year using the increases from the problem.

 Starting SalaryYear 1Year 2Year 3Year 4Year 5
Bob$30,000$33,000$36,000$39,000$42,000$45,000
Jake$20,000$25,000$30,000$35,000$40,000$45,000

 Solution #2: Create an equation using variables.Let x be the number of years after the first year (x=1 is one year later).Bob’s salary = $30,000 (the beginning pay) + $3,000(the increase each year) x (the number of years)Jake’s salary = $20,000 (the beginning pay) + $5,000(the increase each year) x (the number of years)Since we are looking for the year in which both salaries will be equal, set the equations equal to each other. 

30,000 + 3,000x = 20,000 + 5,000x

-20,000                    -20,000________

10,000 + 3,000x  =                   5,000x

                 -3,000x                     -3,000x

10,000                    =                   2,000x

÷2,000                                        ÷2,000   

5                      =                                      x                     So 5 years is the solution.

Problem of the Week Answer

Week #2  

A TV screen measures 24 inches by 16 inches.
If each dimension is increased by 20 percent,by what percent is the area increased?
 

Answer: 44% Solution: 

The first step is to find the new dimensions.  To find the new dimensions you must find 20% of the original dimensions and add that number to the old dimensions.  A quick way to do this is to multiply each dimensions by 1.20 (1 times the original plus 20%)

24 x 1.20 = 28.8                16 x 1.20 = 19.2

So the new dimensions are 24.48 and 16.32.  The question asks for the area, so we must first find the old area (length times width) and the new area.

Old area:  24 x 16 = 384                                                     

New area: 552.96

The problem asks for the percent by which the area was increased.  To find this figure, you must find the amount the area has been increased (new area – old area:  552.96 – 384 = 168.96).  Then divide this number by the original area:  168.96 / 384 = 0.44.

To convert a decimal to a percent, just move the decimal two places to the right, so .44 becomes 44%.

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