Question

Steve buys 7 pens. 7 pencils and 5 marks
amount, which is three-fourths more than what Steve
by Steve is paid for the pens?​

Answer 1

Note: the given question incomplete as its should be,

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?​

Solution:

Assume that the amount paid by Steve is S and the cost of one pen, one pencil, one marker are x,y,z respectively.

According to the question Steve bought 7 pens, 7 pencils and 5 markers.

Therefore, the total amount paid by Steve will be,

$\[7x + 7y + 5z = S - - - - - - \left( 1 \right)\]$

And,

Rick bought 14 pencils, 10 markers and 11 pens.

Therefore, the total amount paid by Rick will be,

$\[\begin{array}{l}11x + 14y + 10x = \frac{3}{4}S + S\\ \Rightarrow 11x + 14y + 10z = \frac{7}{4}S - - - - - - \left( 2 \right)\end{array}\]$

Multiply equation (1) by 2.

$14x+14y+10z=2S------(3)$

Subtract equation (3) and (2).

$\[\begin{array}{l}14x + 14y + 10z - 11x - 14y - 10z = 2S - \frac{7}{4}S\\ \Rightarrow 3x = \frac{1}{4}S\\ \Rightarrow x = \frac{1}{{12}}S\end{array}\]$

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

the percentage of the total amount paid by Steve is paid for the pens is,

$\[ = \frac{x}{S} \times 100\]$

$\[ = \frac{{\frac{1}{{12}}S}}{S} \times 100\]$

$\[ = \frac{1}{{12}} \times 100\]$

$\[ = \frac{{25}}{3}\]$

$\[ = 8.34\% \]$

Hence. the percentage of the total amount paid by Steve is paid for the pens is 8.34%.