Charles wants to buy a sewing machine in a city with a 5% sales tax. He has at most $632 to spend, in what price range should be look?
1.05x = 632
x = 632/1.05 = 601.90
The machine should cost less than 601.90
I am doing something wrong I need some help, I solve as follow:
x+0.05<632
x<632/0.05
x<???????
Thank you Reiny, Why I have to divide 632/1.05? I was dividing 632/0.05, I need to understand for future similar problems, I really appreciate your help, I finished school almost 30 years ago, I decided to go back to school an obtain a degree, I try my best but so many years out of school is challenging.
When you pay for an item with sales tax of 5%
you pay the price + the sales tax
= 100% + 5%
= 1 + .05
= 1.05
similary a sales tax of 7% ---> you pay 1.07
etc
you showed this:
x+0.05<632
x<632/0.05
x<???????
following my argument, you should have had
x + .05x < 632
x is a common factor
x(1 + .05) < 632
x(1.05) < 632
ahhh, now you see where that 1.05 comes from, right ?
Well, Charles better thread carefully and sew some numbers together! If he has $632 to spend, we need to calculate the price range before adding the sales tax. To find that, we'll need to solve a mathematical puzzle. So, let's say x is the price range Charles is looking for. We know that the sales tax is 5%, which is 0.05 in decimal form. If we multiply x by 0.05, we get the amount of tax added to the price. Adding this tax to the price gives us the total amount Charles can spend. So, we can write the equation as:
x + 0.05x = $632
Combining the terms, we have:
1.05x = $632
Now, if we divide both sides by 1.05, we find:
x = $601.90
Therefore, Charles should look for sewing machines in a price range of around $601.90 or less, before the added 5% sales tax. Hoping he "sews" up a great deal!
To calculate the price range Charles should look for, we need to consider the sales tax and the maximum amount he can spend.
Step 1: Calculate the maximum amount he can spend after deducting the sales tax.
To do this, we need to subtract the sales tax from the total amount he has.
Sales tax = 5% = 0.05
Maximum amount Charles has = $632
Deducting the sales tax:
Maximum amount after sales tax = $632 - ($632 * 0.05)
Maximum amount after sales tax = $632 - $31.60
Maximum amount after sales tax = $600.40
So, Charles can spend up to $600.40 after accounting for the sales tax.
Step 2: Determine the price range.
The price range will depend on the sales tax rate and the maximum amount Charles can spend. We need to find the minimum and maximum prices.
Minimum price = Maximum amount after sales tax / (1 + sales tax rate)
Minimum price = $600.40 / (1 + 0.05)
Minimum price = $600.40 / 1.05
Minimum price ≈ $571.33
Maximum price = Maximum amount after sales tax
Maximum price = $600.40
Therefore, Charles should look for a sewing machine in a price range between approximately $571.33 and $600.40.