The sum of the first n positive integers can be found using the formula n(n+1)/2. how many integers must be added to get 253 as the sum.

22

Step-by-step explanation:

Using the given expression and the sum, we can set up an equation and solve for the value of 'n':

Multiply both sides by '2':  

n(n+1) = 506

Distribute: n² + n - 506 = 0

Factor:  (n + 23) (n - 22) = 0

Set each equation equal to '0' and solve:

n + 23 = 0    n - 22 = 0

n = -23   or n = 22

Since the problem says the integers are positive, then n = 22.

Shoes with discount = $17

Necklace = Price * 0.85

Step-by-step explanation:

-If the tennis shoes store sells other things than shoes-

Shoes = $20.00

Discount = 15%

*Price expressed as a percentage*

Price without discount = 100%

Price after discount = 100% - 15%

Price after discount = 85%

*Normal price*

Price without discount = 20

Price after discount = 20 * 0.85

Price after discount = 17