Final answer:
The student spent approximately $1,281.82 on taxable items and $118.18 on sales tax, both rounded to the nearest cent, after using a $1,400 stimulus check with a 9.23% sales tax rate.
Step-by-step explanation:
If a student qualified for the third stimulus check of $1,400 and spent all of it on taxable items with a sales tax rate of 9.23%, we need to calculate both the amount spent on items and the amount spent on sales tax. To begin, we can set up an equation where the total amount spent (items + tax) is equal to $1,400. Let the amount spent on items be 'x' and the sales tax be '0.0923x'. The equation would look like: x + 0.0923x = $1,400.
Solving the equation for 'x' we combine like terms: 1x + 0.0923x = 1.0923x, which gives us 1.0923x = $1,400. Dividing both sides of the equation by 1.0923, we find that x = $1,400 / 1.0923, which calculates to approximately $1,281.82 spent on items before tax. The amount spent on sales tax would then be the total amount minus the amount spent on items: $1,400 - $1,281.82 = $118.18 spent on sales tax.
To summarize, the student would have spent approximately $1,281.82 on items and $118.18 on sales tax, with both values rounded to the nearest cent.