Harry had 2 times as many vacation days as Alex. Kinsey had 3 times a many vacation days as Alex. If Kinsey had 28 vacation days, how many vacation days did Harry have?

Answer 1

I set up the problem with H=2A, K=3A, and K=28d. d is for days.

28/3 = 9.3 It is possible to say wait, these are days and what is 3/10 of a day. You may even begin to convert days into hours by multiplying 28x24 to get a number that when divided by 3 gives a whole number quotient. NO! 672/3 = 224 but you would have taken extra time and it isn't necessary.

Experience with payroll such as you are getting in this problem will inform you that the 3/10 can be rounded to 9 for real pay but for our purposes we will stay with the actual outcomes.

Since 1/3 of what Kinsey has in vacation time is 9.3, we know that Alex's (A) is = 9.3

Harry's therefore is 9.3 x 2 = Harry has 18.6 days for vacation!

The board should look as follows: H=2(9.3) K=3(9.3) and A= 9.3

or H=2A K=3A and A = ?

Answer 2

Write these as equations.

If Harry as twice the vacation days that Alex has, then h=2a. (h for Harry and a for Alex.)

Kinsey has three times as many as Alex. In a similar format, k=3a.

Also, Kinsey has 28, so

k=3a=28

Solve for a:

3a=28, so divide both sides by 3.

a=28/3.

Plugging 28/3 in for Harry's equation, we get h=2(28/3), or h=56/3, which means that

Harry has accrued 18 2/3 days of vacation.

Hope that helps! The numbers come out a little funny, but vacation days do come out like this in actual jobs...

Have fun in algebra, and get in touch if you need more help...