SOLUTION: Kate has 2 more apples than she needs in order to have one-third of the apples that Renee has. Kate is 8 apples short of having half of the apples that Renee has. How many apples d

Question 1036166: Kate has 2 more apples than she needs in order to have one-third of the apples that Renee has. Kate is 8 apples short of having half of the apples that Renee has. How many apples does Kate have?
Found 2 solutions by stanbon, Aldorozos:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Kate has 2 more apples than she needs in order to have one-third of the apples that Renee has. Kate is 8 apples short of having half of the apples that Renee has. How many apples does Kate have?
-----
Equations:
k-2 = (1/3)r
k+8 = (1/2)r
------------
r = 3k-6
r = 2k+16
-----
3k-6 = 2k+16
k = 22 apples (# Kate has)
----------------
Cheers,
Stan H.
-----------
Answer by Aldorozos(172) (Show Source): You can put this solution on YOUR website!
k-2 = 1/3 R
k+8 = 1/2/R
Let's subtract the first equation from the second
k-k + 8-(-2) = 1/2 R - 1/3 r
60 = 1/6 R therefore R = 60 = number of apples Renee has
k+8 = 1/2 60 Therefore K =22
You may check the answer by subtracting 2 from 22 to see if it is 1/3 of 60
RELATED QUESTIONS
One pound of apples is $2. You have no more than $13 to spend on apples. (answered by ikleyn,MathLover1)
Nicole has 3 more dollars than she needs in order to have one-third of the dollars that... (answered by josgarithmetic,ikleyn)
Box A has 128 apples more than Box B. Marcus moved 25% of the apples from Box A to Box... (answered by josmiceli)
Ryan has some bananas. The amount of bananas she has is two more than twice the amount of (answered by josgarithmetic,ikleyn)
The ratio of apples in Barbara's store to those in Mark's store was 8:1. Barbara gave... (answered by josmiceli)
If Sarah had 3 more apples,then she would have three-quarters of the number of apples... (answered by ankor@dixie-net.com)
1. Two numbers are in the ratio 3:7. By adding 10 to each, we get two new numbers in the... (answered by josgarithmetic,ikleyn)
Say Alex has 7 apples less than Barbara, and Barbara has 2 more apples than Casy, but... (answered by richwmiller)
A fruit seller has some apples and pears in the ratio 2:5. He sold 261 pears and bought... (answered by MathTherapy)