0

The price of a TV in 1970 increased by $300$% in 1980. The price of the 1980 model TV increased by $200$% in 1990. By what percentage did the price increase from 1970 to 1990?

Can someone please assist me in doing this? I let the price to be $x$. In 1980, I'm not sure whether it will be $3x$ or $4x$.

Aspiring Mathlete
  • 2,312
  • 1
    it will be $4x$ since it increased by $300%$ – inquisitive Mar 09 '16 at 12:52
  • The question is badly worded. It is asking for the % increase from 1970 to 1990 but only tells us the increases in 1980 and 1990. What about the increase in years 1971, 1972, 1973...1979,1981,1982...1989? If there were increases in those years we need to know. The original question did not state there were increases only in years 1980 and 1990. – David Mar 09 '16 at 13:43

2 Answers2

1

Many times the term increase is misused. Increased by and increased to mean $2$ different things. I can increase my muscle mass to $110$% of what it currently is but I doubt I could increase it by $110$% (thus to $210$% of what it currently is).

For your question, try to find out which they really mean and then solve accordingly. The correct answer should be either $600$% is they use the first interpretation (increased to) or it will be $1200$% if they use the 2nd interpretation (increased by).

F.Y.I., problems like this don't take into account inflation/cost of living increase. For example, if something is $200$ dollars in 1990 it is likely cheaper than that same item being $100$ dollars in 1970 because if the cost of living increased of $4$% per year. $100$ dollars in 1970 would have similar buying power to $219$ dollars in 1990 since $1.04 ^ {20}$ = $2.19$.

Also be careful with problems involving percentages that both increase and decrease because % is a relative operator, not an absolute one. For example, if something is selling for $100$ dollars but sales were sluggish so the manager decided to discount it by $20$% but then it was selling so well at the lower price, decided to increase the price by $20$%, it is then not back to $100$ dollars since $1.2$ * ($100$ dollars * $0.8$) = $96$ dollars.

David
  • 1,702
0

$$P_{1970}=x\\ P_{1980}=(1+300/100)P_{1970}=4x\\ P_{1990}=(1+200/100)P_{1980}=3\cdot 4x=12x$$ When you read such claims e.g. in newspapers, take them with a grain of salt - people rarely take care to use such percentages correctly.

Wouter
  • 7,673