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

sheejave

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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.
 
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Subhotosh Khan

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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.
What are your thoughts?

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Subhotosh Khan

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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/threads/109992-A-wooden-pencil-costs-30-cents-and-a-pen-costs-50-cents
 

sheejave

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55 X no. of pens + 30 X no.of pencils <= 950

I am not sure how to proceed next.

Thanks in advance
 

stapel

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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?"

What is your response? ;)
 

sheejave

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

What is your response? ;)
.55 + .3x <= 9.5

x <= 29.8
 

sheejave

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.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?
 

sheejave

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sheejave

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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
 
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