# Problem of the Week Answers

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?

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

 Starting Salary Year 1 Year 2 Year 3 Year 4 Year 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.

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?

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%.