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%.