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A-dish-of-mixed-nut-contains-cashew-and-peanut-then-two-ounces-of-peanut-are-added-to-the-dish-making-the-new-mixture-of-20-cashew-Sara-like-cashew-so-she-added-2-ounces-of-them-to-the-dish-Th




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 20% cashew.   Sara like cashew so she added   2 ounces of them to the dish. The  mixture in the dish is now  33.33%.   Cashews. what percentage of the   origional mixture of nut was    cashew? this was the correct question  please help
$${A}\:{dish}\:{of}\:{mixed}\:{nut}\:{contains}\:{cashew} \\ $$$${and}\:{peanut}\:.\:{then}\:{two}\:{ounces}\:{of}\: \\ $$$${peanut}\:{are}\:{added}\:{to}\:{the}\:{dish}\:{making} \\ $$$${the}\:{new}\:{mixture}\:{of}\:\mathrm{20\%}\:{cashew}.\: \\ $$$${Sara}\:{like}\:{cashew}\:{so}\:{she}\:{added}\: \\ $$$$\mathrm{2}\:{ounces}\:{of}\:{them}\:{to}\:{the}\:{dish}.\:{The} \\ $$$${mixture}\:{in}\:{the}\:{dish}\:{is}\:{now}\:\:\mathrm{33}.\mathrm{33\%}.\: \\ $$$${Cashews}.\:{what}\:{percentage}\:{of}\:{the}\: \\ $$$${origional}\:{mixture}\:{of}\:{nut}\:{was}\:\: \\ $$$${cashew}?\:{this}\:{was}\:{the}\:{correct}\:{question} \\ $$$${please}\:{help} \\ $$
Answered by MJS last updated on 26/Feb/19
c ounces of cashews and p ounces of peanuts  (c/(c+p+2))=(1/5) ⇒ p=4c−2  ((c+2)/(c+p+4))=(1/3) ⇒ ((c+2)/(5c+2))=(1/3) ⇒ c=2 ∧ p=6  (2/(2+6))=(1/4) ⇒ 25% cashews in the original mix
$${c}\:\mathrm{ounces}\:\mathrm{of}\:\mathrm{cashews}\:\mathrm{and}\:{p}\:\mathrm{ounces}\:\mathrm{of}\:\mathrm{peanuts} \\ $$$$\frac{{c}}{{c}+{p}+\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{5}}\:\Rightarrow\:{p}=\mathrm{4}{c}−\mathrm{2} \\ $$$$\frac{{c}+\mathrm{2}}{{c}+{p}+\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{3}}\:\Rightarrow\:\frac{{c}+\mathrm{2}}{\mathrm{5}{c}+\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}}\:\Rightarrow\:{c}=\mathrm{2}\:\wedge\:{p}=\mathrm{6} \\ $$$$\frac{\mathrm{2}}{\mathrm{2}+\mathrm{6}}=\frac{\mathrm{1}}{\mathrm{4}}\:\Rightarrow\:\mathrm{25\%}\:\mathrm{cashews}\:\mathrm{in}\:\mathrm{the}\:\mathrm{original}\:\mathrm{mix} \\ $$
Commented by otchereabdullai@gmail.com last updated on 26/Feb/19
Thank you MJS Prof
$${Thank}\:{you}\:{MJS}\:{Prof} \\ $$

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