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

Solution

## The correct option is C $$13.5$$Let the cost of Smooth-Glide pens be $$$x$$ andThe 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 $$=$$ $$1\times 9+.50\times 9=9+4.50=13.50$$Mathematics

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