Find the number of pencils and the number of pens that Sharon can buy if she has to b

• 02-02-2018, 11:59 AM
sheejave
Find the number of pencils and the number of pens that Sharon can buy if she has to b
A wooden pencil costs 30 cents and a pen costs 55 cents. Sharon is given \$9.50 and is told to spend the money as much as possible on at least one pencil and at least one pen. However, for every pen that she buys, she must buy at least 3 pencils. Find the number of pencils and the number of pens that Sharon can buy if she has to buy the greatest possible number of items.
• 02-02-2018, 01:35 PM
Subhotosh Khan
Quote:

Originally Posted by sheejave
A wooden pencil costs 30 cents and a pen costs 50 cents. Sharon is given \$9.50 and is told to spend the money as much as possible on at least one pencil and at least one pen. However for every pen that she buys, she must buy at least 3 pencils. Find the number of pencils and number of pens that Sharon can buy if she has to buy the greatest possible number of items.

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

http://www.freemathhelp.com/forum/announcement.php?f=33
• 02-02-2018, 01:37 PM
Subhotosh Khan
Quote:

Originally Posted by sheejave
A wooden pencil costs 30 cents and a pen costs 55 cents. Sharon is given \$9.50 and is told to spend the money as much as possible on at least one pecil and at least one pen. However, for every pen that she buys, she must buy at least 3 3 pencils. Find the number of pencils and the number of pens that Sharon can buy if she has to buy the greatest possible number of items.

Is this the same problem as you had posted before:
https://www.freemathhelp.com/forum/t...costs-50-cents
• 02-02-2018, 02:38 PM
sheejave
55 X no. of pens + 30 X no.of pencils <= 950

I am not sure how to proceed next.

• 02-02-2018, 03:36 PM
stapel
Quote:

Originally Posted by sheejave
55 X no. of pens + 30 X no.of pencils <= 950

I am not sure how to proceed next.

Try following the hint provided earlier: "What happens if Sharon buys only 1 pen?"

• 02-02-2018, 06:22 PM
sheejave
Quote:

Originally Posted by stapel
Try following the hint provided earlier: "What happens if Sharon buys only 1 pen?"

.55 + .3x <= 9.5

x <= 29.8
• 02-02-2018, 06:42 PM
sheejave
Quote:

Originally Posted by sheejave
.55 + .3x <= 9.5

x <= 29.8

0.55 * 2 + 0.3 * x <= 9.5
x = 28

To find the solution of this problem, do you use the trial and error method or is there an algebraic way?
• 02-02-2018, 07:03 PM
sheejave
Quote:

Originally Posted by Denis
Btw, 1st post shows .50 for pens, 2nd shows .55

I am sorry, it's 55 cents
• 02-02-2018, 08:42 PM
sheejave
Quote:

Originally Posted by Denis
Then your x =< 29.8 is correct.
Needs to be rounded down to 29.
1 @ .55 = .55
29 @ .30 = 8.70
.55 + 8.70 = 9.25
9.50 - 9.25 = .25 not spent

The book shows the answer as 2 pens and 28 pencils (you need to spend as much money as possible and buy the greatest possible number of items).

Is there any algebraic method to solve this?

Thanks