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Question 475145: This question read: Without knowing sales tax, find tax on $1500, if tax on $350 is $28. Use proportion to explain. Give real life example of a ratio and a rate. Then explain the difference of each. Why is one a rate and the other a ratio?
Describe steps involved to solve the problem
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you want to find the tax on 1500.
tax on 350 is 28 dollars.
rate of tax on 350 is 28/350 = .08
apply this rate to 1500 and you get .08 * 1500 = 120.
I found the rate and then applied it.
If I did it another way, then I would be taking the ratio and applying it.
The other way would be done as follows:
28/350 = x/1500
Now this is a ratio and not a rate since I don't know the rate because I didn't solve for it.
I multiply both sides of this equation by 1500 to get:
x = 28/350 * 1500 = 120.
I get the same tax.
In the first case, I solved for the rate and then applied the rate to $1500 in order to get the tax of $120.
In the second case, I applied the ratio of 28 is to 350 as x is to 1500 in order to derive the tax.
It's a technicality.
In the first case I knew what the rate was because I solved for it.
In the second case I didn't know what the rate was but applied the ratio to find the tax.
Note that in the second case I didn't know what the rate was even though the ratio of 28/350 could have been used to solve for the rate if I wanted to find out what that was first.
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