Question

A student bought some pens at 8 each and some pencils at 1.50 each. If the total
number of pens and pencils purchased is 16 and their total cost is 50, how many pens
did he buy?
his​

Answer 1

Step-by-step explanation:

Given:-

• A student bought some pens at 8 each and some pencils at 1.50 each.

• The total number of pens and pencils is 16.

• And their total cost = Rs.50

To Find:-

• The number of pens bought by him.

Solution:-

Let the number of pens be x

And number of pencils be y

The total number of pens and pencils is 16.

$\sf \implies x + y = 16.....(i)$

Total cost = Rs.50

$\sf \implies 8x + 1.5y = 50.....(ii)$

Multiply equation (i) with 8:-

$\sf \implies 8(x + y = 16)$

$\sf \implies 8x + 8y = 128....(iii)$

Equation (iii) - (ii)

$\sf \implies 8x + 8y - (8x + 1.5y) = 128 - 50$

$\sf \implies 8x + 8y - 8x - 1.5y = 78$

$\sf \implies 6.5y = 75$

$\sf \implies y = \dfrac{75}{6.5}$

$\sf \implies y = 12$

Substitute y = 12 in equation (i)

$\sf \implies x + y = 16$

$\sf \implies x + 12 = 16$

$\sf \implies x = 4$

$\large\underline{\boxed{\therefore \textsf{\textbf{Total \: number \: of \: pens = 4}}}}$

Answer 2

Answer

:

$\huge \bf \: Given$

Rupees of each pen = 8

Rupees of each pencil = 1.50

Total things purchased = 16

Total cost = 50

$\huge \bf \: To \: find$

Total pen she buy

$\huge \bf \: Solution$

$\huge \tt \: Let$

Pen = x

Pencil = y

Therefore,

$\tt \implies \: x \: + y = 16 \:....(EQ \: 1)$

$\tt \implies \: 8x + 1.5y = 50 (EQ 2)$

Now,

Multiplying EQ 1 with 8

$\sf \: 8(x + y = 16)$

$\sf \: 8x + 8y = 128.... (iii)$

Equation (iii) - (ii)

$\sf 8x+8y−(8x+1.5y)=128−50$

$\sf \: 8x+8y−8x−1.5y=78$

$\sf \:6.5 y = 75$

$\sf \: y \: = \dfrac{75}{6.5}$

$\sf \: y \: = 12$

Now,

Substituting y = 12 from EQ 1

$\sf \: x \: + y = 16$

$\sf \: x + 12 = 16$

$\sf \: x = 16 - 12$

$\sf \: x = 4$

${\huge {\fbox {pens \: = 4}}}$