Firewood Processor Forum

1) Given f(x)=(x-8)/4 and g(x)=4x+8, find (g of f)(x).

2) A chemist needs 11 liters of a 50% salt solution. All she has available is a 20% salt solution and a 70% salt solution. How many liters of the 20% solution should she mix to obtain her desired solution?

3.) Change the equation to logarithmic form: 7^x=9.8

4.) Working with your cousin, you can split a cord of firewood in 5 hours. Working alone, your cousin can complete the job in 7 hours. How long would it take you to split the firewood working alone?

1) g(f(x))= (4x+8-8)/4= x
3) x= (log 9.8)/(log 7)= log 2.8
4) well,in one hour, you can split 1/5 the work and your cousin can do 1/7 of the work so add those two up in one hour you and your cousin will do 12/35 of the work. so if you and your cousin work together it will take 1/(12/35)= 35/12 hours
2) liters for 20% is a, 70% is b, we have two functions:
a+b=11
0.2a+0.7b= 5.5
so b=11-a
=> 0.2a+ 0.7(11-a)=5.5
=>0.2a+7.7-0.7a=5.5
=> -0.5a= -2.2a
=>a= 4.4
=>b=11- 4.4= 6.6 (1 billion:)) )(just kidding!just for fun,no money needed)