In this question, it is given that
Leanne has a gas card that has $150 on it. She spends $25 a week on gas.
And we have to Write a recursive rule that represents the amount of money she has on her gas card after the first week .
Recursive rule shows the relationship between previous value and the current value .
And here, the recursive rule is

Where a(n-1) is the initial amount which is $150 . And a(n) is the amount after n week .
So for n=1, that is amount in the card after 1 week, we will get

And that's the amount remaining in the card after 1 week .
32 grams = water mass + sugar mass . 100% syrup=75% water+ 25%sugar
original water content= 32*75/100=24 grams
original sugar content= 32*25/100= 8grams
total mass at 10% syrup:
8grams/total mass=10%=0.1
total mass=8/0.1=80grams
total mass of water=80grams- 8grams of sugar content= 72 grams
total mass of water added=72grams- 24grams original water content= 48grams.
answer: 48grams
Joe runs one lap around a track in 80 seconds. Joe and Jim meet after 30 seconds.We know how long does it take for Joe to run one lap, so we can calculate what distance he runs in 30 seconds:
He runs half lap for 40 seconds. He runs quarter lap for 20 minutes and he runs 1/8 lap for ten minutes. So for 30 seconds he runs 3 * 1/8 lap=3/8 lap.
Because Jim runs in opposite direction this means that he will meat with Joe at 1-3/8=5/8 lap. So, Jim runs 5/8 lap for 30 seconds.
1/8 lap Jim runs for 30/5=6 seconds, so Jim needs 8*6=48 seconds to run the lap.
After 30 seconds Joe has run e runs
1. 8(1+2)........................................