Question

Twelve Smooth-Glide pens and eight Easy-Write pencils cost exactly $\$16.00$ at Office World. Six Smooth-Glide pens and ten Easy-Write pencils cost $\$11.00$ at the same location. How much will nine Smooth-Glide pens and nine Easy-Write pencils cost at Office World?

• A. $13.5$
• B. $12$
• C. $13$
• D. $15$

Answer 1

Answer: (A)

$13.5$

Let the cost of Smooth-Glide pens be x$ and

The cost of Easy-write pencils cost be y$

The according to the question,

$\Rightarrow 12x+8y=16$.........(1)

$\Rightarrow 6x+10y=11$..........(2)

Multiply the (1) by $10$ and (2) by $8$, we get

$\Rightarrow 120x+80y=160$.........(3)

$\Rightarrow 48x+80y=88$...........(4)

Subtract the (3) and (4), we get

$\Rightarrow 72x=72$

$\Rightarrow x=$1$

Sustitute the value of $x=1$ in (1)

$\Rightarrow 12\times 1+8y=16$

$\Rightarrow 8y=16-12$

$\Rightarrow y=\frac{4}{8}=\frac{1}{2}=$.50$

Then cost of $9$ Smooth-Glide pens and $9$ Easy-Write pencils $=$ $1\times 9+.50\times 9=9+4.50=13.50$