Solve the following application problem. Murray’s Music sells a guitar for $349.85 while using a markup of 21% on cost. Find the cost.

Question

When I solve this problem, I somehow got the wrong answer even though I looked in the textbook for step by step. Still go the wrong answer. 

Answer 1

 

This one is much simpler than it looks, once you know the trick. So the first number that we're given, $349.85, is how much the guitar sells for, the second number of 21% tells us what percentage the item is marked up. If you think about this plainly, it makes sense that the true cost an item could be proportionately represented by 100%, or 1. In this situation, the item is marked up 21%, or .21. By adding the markup to the original cost, we can say that the guitar is being sold at 121%, or 1.21, of its original cost. That part may seem easy when you think about it, the next is almost as simple. We want to reduce the number we are given from 121% to 100% to find the cost of the guitar before markup. To do this, convert the percentages to numbers and divide them. So we take 100% and turn it into 1, and turn 121% into 1.21 and divide the former by the latter.

 

(1/1.21) x 349.85 = 289.13 [the original cost of the guitar when rounded to the nearest cent]. We can check the math by adding 21% to the original cost of 289.13. To do this simply, we multiply 289.13 by 1.21 (or 121%), and we get the sale price of 349.85 (after rounding to the nearest cent).