Answer:
g = 6
Step-by-step explanation:
5.2g + 10 = 2.2g + 28 (Given)
3g + 10 = 28 (Subtracted 2.2g on both sides)
3g = 18 (Subtracted 10 on both sides)
g = 6 (Divided 3 on both sides)
To check to make sure you are correct, simply substitute your answer for g:
5.2(6) + 10 = 2.2(6) + 28
31.2 + 10 = 13.2 + 28
41.2 = 41.2
You'll know you're correct if they both equal the same. In this case, the solution works.
If you are asking how much he still has well he would still have 32.75
Rewrite each given equation as
![p=q^r\implies \log_p(p)=\log_p(q^r)\implies 1=r\log_p(q)\implies r=\dfrac1{\log_p(q)}=\dfrac{\ln(q)}{\ln(p)}](https://tex.z-dn.net/?f=p%3Dq%5Er%5Cimplies%20%5Clog_p%28p%29%3D%5Clog_p%28q%5Er%29%5Cimplies%201%3Dr%5Clog_p%28q%29%5Cimplies%20r%3D%5Cdfrac1%7B%5Clog_p%28q%29%7D%3D%5Cdfrac%7B%5Cln%28q%29%7D%7B%5Cln%28p%29%7D)
![q=r^p\implies \log_q(q)=\log_q(r^p)\implies 1=p\log_q(r)\implies p=\dfrac1{\log_q(r)}=\dfrac{\ln(r)}{\ln(q)}](https://tex.z-dn.net/?f=q%3Dr%5Ep%5Cimplies%20%5Clog_q%28q%29%3D%5Clog_q%28r%5Ep%29%5Cimplies%201%3Dp%5Clog_q%28r%29%5Cimplies%20p%3D%5Cdfrac1%7B%5Clog_q%28r%29%7D%3D%5Cdfrac%7B%5Cln%28r%29%7D%7B%5Cln%28q%29%7D)
![r=p^q\implies \log_r(r)=\log_r(p^q)\implies 1=q\log_r(p)\implies q=\dfrac1{\log_r(p)}=\dfrac{\ln(p)}{\ln(r)}](https://tex.z-dn.net/?f=r%3Dp%5Eq%5Cimplies%20%5Clog_r%28r%29%3D%5Clog_r%28p%5Eq%29%5Cimplies%201%3Dq%5Clog_r%28p%29%5Cimplies%20q%3D%5Cdfrac1%7B%5Clog_r%28p%29%7D%3D%5Cdfrac%7B%5Cln%28p%29%7D%7B%5Cln%28r%29%7D)
where each of the last equalities follows from the change-of-base identity,
![\log_m(n)=\dfrac{\log_b(n)}{\log_b(m)}](https://tex.z-dn.net/?f=%5Clog_m%28n%29%3D%5Cdfrac%7B%5Clog_b%28n%29%7D%7B%5Clog_b%28m%29%7D)
for any base <em>b</em> > 0 and <em>b</em> ≠ 1. I picked the natural base, <em>e</em>.
Then
![prq=\dfrac{\ln(r)}{\ln(q)}\times\dfrac{\ln(q)}{\ln(p)}\times\dfrac{\ln(p)}{\ln(r)}=1](https://tex.z-dn.net/?f=prq%3D%5Cdfrac%7B%5Cln%28r%29%7D%7B%5Cln%28q%29%7D%5Ctimes%5Cdfrac%7B%5Cln%28q%29%7D%7B%5Cln%28p%29%7D%5Ctimes%5Cdfrac%7B%5Cln%28p%29%7D%7B%5Cln%28r%29%7D%3D1)
as required.
First we get 30% ounces of peanuts in mixed nuts:
(0.3) * (32) = 9.6
To find the percentage of peanut concentration of the final mix if you add x ounces of peanuts:
% of peanuts = ((x + 9.6) / (x + 32)) * (100)
Answer:
An expression can be used is:
% of peanuts = ((x + 9.6) / (x + 32)) * (100)