Ellen has a gift card to Target for $50. She didn't want to go over the $50 and be embarrassed having to put back items, so she kept a running total estimate in her head while she shopped. In her cart, she had a sweater for $15.99, a pop socket for $9.99, a DVD for $7.99, and a new book by her favorite author for $12.99. (Note: tax is 5.5% where Ellen lives). She estimated 47 before tax. Ellen was shocked when the cashier told her that the total was $55.54.

Who did something wrong? Did Ellen round incorrectly somewhere, or did the cashier punch something wrong into the cash register? Show your work and describe how you arrived at your answer.

The cashier must have calculated wrong.

Step-by-step explanation:

To add everything up (like Ellen did), we can round to make it easier, as we don't need an exact amount.

16+10+8+13

16 + 10 = 26, 26 + 8 = 34, 34 + 13 = 47

So, from this we got that Ellen is correct in her estimation.

Now, we need to calculate tax. First, we need to find 5.5% of 47. Again, the numbers don't need to be exact for this problem, if we account for it at the end.

47 x. 055 = 2.585

This means that about $2.50 will be added onto for tax. In reality it is probably a couple cents less, because we rounded all of those other numbers up.

Add this onto the estimated total before tax.

47 + 2.5 = 49.5, or $49.50

Our final conclusion is that Ellen still has enough money to pay for the item. The cashier must have done something incorrectly.