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 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.__

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%.