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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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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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/...encil-costs-30-cents-and-a-pen-costs-50-cents
 
55 X no. of pens + 30 X no.of pencils <= 950

I am not sure how to proceed next.

Thanks in advance
 
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? ;)
 
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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