Finding the mistake

Question

Mark solved  the following problem as shown below:

Gas prices are projected to increase by 124% by April 2016, a gallon of gas currently cost $2.90.

What is the projected cost of a gallon of gas for April 2016?

1.24(2.90)=3.596=$3.60

The projected cost of a gallon of gas for April 2016 is $3.60.

What mistake did Mark make? Explain what his misunderstanding was, then correctly find the projected cost of a gallon of gas for April 2016.

Answer 1

This is an example of a poorly worded problem. 

"Increased 124%" is different than "increased by 124%."

Mark (great name) understood the problem to mean "increased 124%" and correctly calculated.

Since this is in error, the expected interpretation must be "increased by 124%" therefore the price increased by $3.60 giving a project price of $6.50.

Answer 2

The error was that the Mark of the problem (not the tutor) calculated the final price as if the price increased to 124% of the original, which means it increased by 24%, not by 124%.  The correct way to work the problem is to assume the price increased to 124% above its original level.  That means you have to multiply the original level by (1+ 1.24) = 2.24

 

Final price = (2.24)($2.90) ≅ $6.50

 

That is the answer both tutors got.

Answer 3

He made a mistake with the tax rate.  He needs to multiply that tax by the original cost.

 

tax rate = 1 + 1.24

            = 2.24

 

Project cost = $2.90(2.24)