Activity › Discussion › Math › Algebraic equation
Tagged: algebra

Algebraic equation
Posted by Aanya Triv on June 24, 2023 at 5:09 pmAnn went to a shop to buy 2 pens and 5 pencils. If the cost of 2 pens was 30 rupees and total amount of her purchase was 80 rupees. How much did each pen and pencil cost?
Padma Pasu replied 1 year, 3 months ago 3 Members · 2 Replies 
2 Replies

::
Let, the cost of pen and pencil be x and y respectively (x>=0 , y>=0)
cost of 2 pens is Rs. 30 (Given)
<b class=””>∴ 2x=30
<b class=””><b style=”fontfamily: inherit; fontsize: inherit; color: var(–bbbodytextcolor);”> ⇒ <b style=”fontfamily: inherit; fontsize: inherit; color: var(–bbbodytextcolor);”>x=15
cost of 2 pens and 5 pencils is Rs. 80 <b style=”fontfamily: inherit; fontsize: inherit; color: var(–bbbodytextcolor);”>(Given)
∴ 2x+5y=80 ⟶eqn(i)
Putting the value of x=15 in eqn(i), we get
30+5y=80
<b style=”fontfamily: inherit; fontsize: inherit; color: var(–bbbodytextcolor); backgroundcolor: var(–bbcontentbackgroundcolor);”>⇒ 5y=8030
⇒ y=50/5
⇒ y=10
Hence, the cost of 1 pen is Rs. 15 and the cost of 1 pencil is Rs. 10.

::
Ann went to a shop to buy 2 pens and 5 pencils. If the cost of 2 pens was 30 rupees and total amount of her purchase was 80 rupees. How much did each pen and pencil cost?
Solution:
Let x be the cost of a pen.
Let y be the cost of a pencil.
The cost of 2 pens are 30 Rs.
So,the algebraic expression is
2x = 30
x = 30/2 = 15
The cost of a pen = 15 Rs
Ann purchase 2 pens and 5 pencils in total amount 80 Rs.
So, the algebraic expression is
2x+5y = 80
2*15+5y = 80
30+5y = 80
5y = 8030
5y = 50
y = 50/5 = 10
The cost of a pencil = 10 Rs
Answer:
The cost of a pen = 15 Rs
The cost of a pencil = 10 Rs
👍
Log in to reply.