homework help.

Question

Rachel's health-related budget is as follows:
-The percentage budgeted for health insurance is four times the percentage for health club dues.
-The percentage budgeted for prescriptions is equal to 1/4 the percentage budgeted for health insurance.
-The percentage budgeted for doctor visits is twice the percentage budgeted for prescriptions.

What is the percentage for prescriptions?

Answer 1

Let h be the percentage for health insurane

Let p be the percentage for prescriptions

Let c be the percentage for health club fees

Let d be the percentage for doctor visits.

 

 So, h= 4c or c= (1/4)h, the club fees are 1/4 of the health care fees

 P= (1/4)h, percriptions are 1/4 of the health fees

 

 d= 2p, and we know that p= (1/4)h. So, substituting (1/4)h for p, we get, d= 2(1/4)p or d= 1/2 h

 

Thus, h+p+c+d= 1, one hundred percent

substituting and solving in terms of h, we get

 

h+(1/4)h+ (1/4)h+ (1/2)h = 1

2h= 1

h= .5  

 

Now that we know that h=.5, we plug in .5 into p= (1/4) h.  Or p= (1/4)(1/2)= 1/8 or 12.5 %. So, she spends 12.5% on prescriptions. 

 

Read it slowly, and you will get it. :)

 

 

Answer 2

Let:

i = the percent for health insurance

c = the percent for club dues

p = the percent for prescriptions

d = the percent for doctor visits

 

i + c + p + d = 1 (100%)

 

i = 4c

p = i/4 = 4c/4 = c      [Since i = 4c]

d = 2p

 

Let's substitute:

i + c + p + d = 1

4p + p + p + 2p = 1            [i=4c=4p, c=p, d=2p]

8p = 1

p = 1/8 = 0.125 = 12.5%

 

The other percents are:

c = p = 12.5%

d = 2p = 2*12.5% = 25%

i = 4c = 4*12.5% = 50%

 

Check:

i + c + p + d = 100%

50% + 12.5% + 12.5% + 25% = 100%

100% = 100%

Check!