Question Number 55534 by otchereabdullai@gmail.com last updated on 26/Feb/19
$${A}\:{dish}\:{of}\:{mixed}\:{nut}\:{contains}\:{cashew} \\ $$$${and}\:{peanut}\:.\:{then}\:{two}\:{ounces}\:{of}\: \\ $$$${peanut}\:{are}\:{added}\:{to}\:{the}\:{dish}\:{making} \\ $$$${the}\:{new}\:{mixture}\:{of}\:\mathrm{20\%}\:{cashew}.\: \\ $$$${Sara}\:{like}\:{cashew}\:{so}\:{she}\:{added}\: \\ $$$$\mathrm{2}\:{ounces}\:{of}\:{them}\:{to}\:{the}\:{dish}.\:{The} \\ $$$${mixture}\:{in}\:{the}\:{dish}\:{is}\:{now}\:\:\mathrm{33}.\mathrm{33\%}.\: \\ $$$${Cashews}.\:{what}\:{percentage}\:{of}\:{the}\: \\ $$$${origional}\:{mixture}\:{of}\:{nut}\:{was}\:\: \\ $$$${cashew}?\:{this}\:{was}\:{the}\:{correct}\:{question} \\ $$$${please}\:{help} \\ $$
Answered by MJS last updated on 26/Feb/19
$${c}\:\mathrm{ounces}\:\mathrm{of}\:\mathrm{cashews}\:\mathrm{and}\:{p}\:\mathrm{ounces}\:\mathrm{of}\:\mathrm{peanuts} \\ $$$$\frac{{c}}{{c}+{p}+\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{5}}\:\Rightarrow\:{p}=\mathrm{4}{c}−\mathrm{2} \\ $$$$\frac{{c}+\mathrm{2}}{{c}+{p}+\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{3}}\:\Rightarrow\:\frac{{c}+\mathrm{2}}{\mathrm{5}{c}+\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}}\:\Rightarrow\:{c}=\mathrm{2}\:\wedge\:{p}=\mathrm{6} \\ $$$$\frac{\mathrm{2}}{\mathrm{2}+\mathrm{6}}=\frac{\mathrm{1}}{\mathrm{4}}\:\Rightarrow\:\mathrm{25\%}\:\mathrm{cashews}\:\mathrm{in}\:\mathrm{the}\:\mathrm{original}\:\mathrm{mix} \\ $$
Commented by otchereabdullai@gmail.com last updated on 26/Feb/19
$${Thank}\:{you}\:{MJS}\:{Prof} \\ $$