Question

Steve buys 7 pens, 7 pencils and 5 markers. Rick buys 14 pencils, 10 markers and 11 pens for an amount, which is three-fourths more than what Steve pays. What percentage of the total amount paid by Steve is paid for the pens?​

Answer 1

        $\text{\huge \bf \underline{Answer:}}$

        $\text{Let the amount payed by Steve be }S$

        $\text{Let the cost of one pen, pencil and marker be }x,y \text{ and }z \text{ respectively}$

        $\text{It is given that Steve bought 7 pens 7 pencils and 5 markers}$

$\implies \: \text{The total amount payed by Steve} = 7x + 7y + 5z = S$

$\implies \: 7x + 7y + 5z = S \text{ ------ (i)}$

        $\text{It is given that Rick bought 11 pens 14 pencils and 10 markers}$

        $\text{It is also given that Rick payed three-fourths more than Steve}$

$\implies \: \text{The total amount payed by Rick} = 11x + 14y + 10z = \dfrac{3}{4}S +S$

$\implies \: 11x + 14y + 10z = \dfrac{7}{4}S \text{ ------ (ii)}$

        $\text{Multiplying (i) by 2}$

$\implies \: 14x + 14y + 10z = 2s \text{ ------ (iii)}$

        $\text{Substracting (ii) from (iii)}$

$\implies \: 14x + 14y + 10z - 11x - 14y - 10z = 2S - \dfrac74S$

$\implies \: 3x = \dfrac14S$

$\implies \: x = \dfrac1{12}S \text{ ------ (iv)}$

$\implies \:\text{Percentage} = \dfrac{x}{S} \times 100$  

        $\text{From (iv)}$

$\implies \:\text{Percentage} = \dfrac{\dfrac{1}{12}S}{S} \times 100$

$\implies \:\text{Percentage} = \dfrac{1}{12} \times 100$

$\implies \: \text{Percentage} = \dfrac{25}{3}$

$\implies \: \text{Percentage} = 8.333 \: \%$

$\implies \: \boxed{\boxed{\text{Percentage} = 8.34 \: \% \: \text{(approx.)}}}$

Answer 2

Given:

Steve buys 7 pens, 7 pencils and 5 markers

Rick buys 14 pencils, 10 markers and 11 pens

Find percentage of the total amount paid by Steve is paid for the pens = ?

Solution:

Let amount paid by Steve be "S"

Let cost of pen, pencil, and marker be x, y, z respectively.

• According to question we have,

• The total amount paid by Steve = S = 7x + 7y + 5z           -(1)

Given that Rick buys 14 pencils, 10 markers and 11 pens

Also given that Rick paid three-fourths more than Steve

• The total amount paid by Rick = 11x + 14y + 10z = $\frac{3}{4}S + S$      -(2)

Multiply equation (1) by 2

=>  14x + 14y + 10z = 2S       -(3)

Substitution equation (2) from equation (3) we get

=>  14x + 14y + 10z - 11x - 14y - 10z = 2S - $\frac{3}{4}S -S$

=>  $3x = 2S -\frac{7}{4}S\\\\3x = \frac{8S - 7S}{4} \\\\3x =\frac{1}{4}S\\\\x= \frac{1}{3\times4}S\\\\x=\frac{1}{12}S$

$Percentage = \frac{x}{S}\times100$

=>  Substituting value of x

$Percentage = \frac{\frac{1}{12}S }{S}\times100\\\\Percentage = \frac{1}{12} \times100\\\\Percentage = \frac{25}{3} \\\\Percentage = 8.33\%$

Hence the percentage is 8.33%