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Question Number 108917 by pete last updated on 20/Aug/20

A woman purchased a number of plates  for$150.00. Four of the plates got broken  while transporting themto her shop. By selling  the remaining plates at a profit of $ 1.00 on each,  she made a total profit of $6.00. How many  plates did she purchase?

$$\mathrm{A}\:\mathrm{woman}\:\mathrm{purchased}\:\mathrm{a}\:\mathrm{number}\:\mathrm{of}\:\mathrm{plates} \\ $$$$\mathrm{for\$150}.\mathrm{00}.\:\mathrm{Four}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plates}\:\mathrm{got}\:\mathrm{broken} \\ $$$$\mathrm{while}\:\mathrm{transporting}\:\mathrm{themto}\:\mathrm{her}\:\mathrm{shop}.\:\mathrm{By}\:\mathrm{selling} \\ $$$$\mathrm{the}\:\mathrm{remaining}\:\mathrm{plates}\:\mathrm{at}\:\mathrm{a}\:\mathrm{profit}\:\mathrm{of}\:\$\:\mathrm{1}.\mathrm{00}\:\mathrm{on}\:\mathrm{each}, \\ $$$$\mathrm{she}\:\mathrm{made}\:\mathrm{a}\:\mathrm{total}\:\mathrm{profit}\:\mathrm{of}\:\$\mathrm{6}.\mathrm{00}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{plates}\:\mathrm{did}\:\mathrm{she}\:\mathrm{purchase}? \\ $$

Answered by nimnim last updated on 20/Aug/20

Let the total number of plates be x  then CP of 1 plate=$((150)/x)  since 4 plates had been broken,  SP of (x−4) plates⇒(x−4)(((150)/x)+1)=156  ⇒x^2 +146x−600=156x  ⇒x^2 −10x−600=0  ⇒(x−30)(x+20)=0  ⇒x=30  or  x=−20(neclegted)  Hence, the woman purchased 30 plates

$${Let}\:{the}\:{total}\:{number}\:{of}\:{plates}\:{be}\:{x} \\ $$$${then}\:{CP}\:{of}\:\mathrm{1}\:{plate}=\$\frac{\mathrm{150}}{{x}} \\ $$$${since}\:\mathrm{4}\:{plates}\:{had}\:{been}\:{broken}, \\ $$$${SP}\:{of}\:\left({x}−\mathrm{4}\right)\:{plates}\Rightarrow\left({x}−\mathrm{4}\right)\left(\frac{\mathrm{150}}{{x}}+\mathrm{1}\right)=\mathrm{156} \\ $$$$\Rightarrow{x}^{\mathrm{2}} +\mathrm{146}{x}−\mathrm{600}=\mathrm{156}{x} \\ $$$$\Rightarrow{x}^{\mathrm{2}} −\mathrm{10}{x}−\mathrm{600}=\mathrm{0} \\ $$$$\Rightarrow\left({x}−\mathrm{30}\right)\left({x}+\mathrm{20}\right)=\mathrm{0} \\ $$$$\Rightarrow{x}=\mathrm{30}\:\:{or}\:\:{x}=−\mathrm{20}\left({neclegted}\right) \\ $$$${Hence},\:{the}\:{woman}\:{purchased}\:\mathrm{30}\:{plates} \\ $$

Commented by pete last updated on 20/Aug/20

iThank you sir

$$\mathrm{iThank}\:\mathrm{you}\:\mathrm{sir} \\ $$

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