Question

Last year Nancy’s annual salary was x dollars. This year she received a raise of y dollars per year. She is paid semimonthly. a. Express her semimonthly salary last year algebraically. b. Express her semimonthly salary this year algebraically. c. On a monthly basis, how much more does Nancy earn as a result of her raise?

Answer 1

a. x/24

b. (x+y)/24

c. y/12

Explanation:

semimonthly = twice a month or 24 times a year (because 12 months * twice a month = 24 times)

a. as she was paid 24 times a year for x dollars last year,

24 semimonthly payments of d dollars = x

divide both sides by 24 to get d

x / 24 = d dollars per semimonthly payment

b. she is paid x + y dollars this year, so she is paid (x+y)/24 dollars for her semimonthly salary

c. she earns y additional dollars per year. divide by 12 (because 12 months = 1 year) to get one month's worth of additional dollars = y/12 dollars extra per month