Please help!! I’ve tried to answer this but I’m off a few cents every time. Megan’s aunt have her a $100 gift card to Toys R Us for her birthday. Determine the price of the most expensive toy that Megan can buy with this gift card if the sales tax is currently 9.8%

$91.07

Step-by-step explanation:

You cannot take off 9.8% from $100 to find the answer, since 9.8% of $100 is more tax than she will pay. The toy has to cost less than $100, so that when you add 9.8% tax the price you end up with exactly $100, and 9.8% of under $100 is less that 9.8% of $100. Maybe this is why you are a few cents off.

This is how you do it.

The price of the toy is unknown, so we'll cal it x.

When you add 9.8% tax to x, you want to end up with exactly $100.

x + 9.8% of x = 100

Write 9.8% as a decimal by dividing the percent by 100.

9.8% = 9.8/100 = 0.098

Now we have:

x + 0.098x = 100

Add like terms on the left side:

1.098x = 100

Divide both sides by 1.098:

x = 100/1.098

x = 91.07

The most expensive toy she can get costs $91.07 before tax.

Check:

We now add 9.8% tax to $91.07 and make sure the total cost including tax  is no more than $100.

$91.07 + 9.8% of $91.07 =

= $91.07 + 0.098 * $91.07

= $91.07 + $8.92

= $99.99

It seems that you could try to spend one more cent, to really get to the $100 limit, so let's try $91.08 as the most expensive toy she can buy.

We now add 9.8% tax to $91.08 and see what the total cost including tax is.

$91.08 + 9.8% of $91.08 =

= $91.08 + 0.098 * $91.08

= $91.08 + $8.93

= $100.01

You see that if Megan gets a $91.08 toy, with tax, the total cost is $100.01, which is over the $100 limit, so the answer is indeed $91.07.