Use proportional relationships to solve the following problem. Riley needs to earn enough money to purchase a new jacket. The one he likes best is $49.99. His state sales tax is 7.25%. How much money does he need to earn? Round to the nearest dollar.(1 point)
Responses
$82
$82
$50
$50
$3.62
$3.62
$54
$54
To solve this problem using proportional relationships, we can set up the following equation:
x + 0.0725x = 49.99
Where x represents the amount of money Riley needs to earn before tax.
Simplifying the equation, we have:
1.0725x = 49.99
Dividing both sides of the equation by 1.0725, we get:
x = 49.99 / 1.0725
x ≈ 46.64
Therefore, Riley needs to earn approximately $46.64 before tax.
To find the total amount of money he needs to earn including tax, we can calculate:
46.64 + (0.0725 * 46.64) ≈ 46.64 + 3.38
Rounding to the nearest dollar, Riley needs to earn approximately $50 in total.
To solve this problem, we need to use the concept of proportional relationships. A proportional relationship means that two quantities are related in a consistent way. In this case, the price of the jacket and the amount of money Riley needs to earn are related proportionally.
First, we need to find the amount of money Riley needs to earn to cover the cost of the jacket before sales tax. We can set up a proportion:
Cost of jacket (before tax) / Amount of money Riley needs to earn = Proportion constant
Let's call the amount of money Riley needs to earn "x" dollars. We can set up the proportion as:
49.99 / x = Proportion constant
To find the proportion constant, we divide the cost of the jacket by the amount of money Riley needs to earn:
Proportion constant = 49.99 / x
Now, let's calculate the sales tax. The state sales tax rate is 7.25%. To find the amount of sales tax, we multiply the cost of the jacket by the sales tax rate:
Sales tax = 49.99 * 0.0725
We add the sales tax to the cost of the jacket to find the total cost:
Total cost of jacket = 49.99 + (49.99 * 0.0725)
Now, we have the proportion constant and the total cost of the jacket. We can set up another proportion to find the value of "x" (the amount of money Riley needs to earn):
Total cost of jacket / Amount of money Riley needs to earn = Proportion constant
Plugging in the values, we get:
(49.99 + (49.99 * 0.0725)) / x = Proportion constant
Simplifying the equation, we have:
(Rounded to nearest dollar) x = 54
Therefore, the correct answer is $54. Riley needs to earn $54 to purchase the new jacket, rounded to the nearest dollar.
Rafeal’s family dinner costs $56.25. His dad wants him to leave a 35% tip. How much money should Rafeal provide as a tip? Round your answer to the nearest hundredth.(1 point)
Responses
$1.97
$1.97
$75.94
$75.94
$35.00
$35.00
$19.69