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 $4x$.
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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.
$$P_{1970}=x\\ P_{1980}=(1+300/100)P_{1970}=4x\\ P_{1990}=(1+200/100)P_{1980}=3\cdot 4x=12x$$ 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.