Tip at Restaurant Question

[mathilliterate8]

Assuming a tip of 20%, what would the pre-tip total have to be for the final total (including tip) to be exactly $100. I was able to determine the answer through trial and error, but how would you solve this without trial and error?

My thinking is:

100 = x + (x)(.2)

where x = the tip-tip total

100 = the total with tip included

But that might be totally wrong.

And if it's the right equation, I still don't know how to solve it.

 

[Deleted member 4993]

Assuming a tip of 20%, what would the pre-tip total have to be for the final total (including tip) to be exactly $100. I was able to determine the answer through trial and error, but how would you solve this without trial and error?

My thinking is:

100 = x + (x)(.2) ....................... correct

where x = the tip-tip total

100 = the total with tip included

But that might be totally wrong.

And if it's the right equation, I still don't know how to solve it.

100 = x + (x)(.2)

100 = x * [1 + (.2)] ...............factoring out 'x'

continue......

 

[mathilliterate8]

100 = x + (x)(.2)

100 = x * [1 + (.2)] ...............factoring out 'x'

continue......

Yes, after giving it some thought I think I figured it out

100 = 1.2x

100 / 1.2 = 1.2x / 1.2

83.33 = x

 

[lookagain]

Yes, after giving it some thought I think I figured it out

100 = 1.2x

100 / 1.2 = 1.2x / 1.2

83.33 = x

That is correct to the nearest hundredth.


The pre-tip total is exactly $83.33.

($83.33)(20%) = $16.666

This rounds up to an exact tip of $16.67.


The pre-tip total of exactly $83.33, plus the tip of exactly $16.67, add up to exactly $100.