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

1. ## 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. 2. 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.

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3. 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

4. Hint: what happens if Sharon buys only 1 pen?

5. 55 X no. of pens + 30 X no.of pencils <= 950

I am not sure how to proceed next.

6. 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?"

7. Btw, 1st post shows .50 for pens, 2nd shows .55

8. 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

9. 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?

10. PLEASE confirm: are pens 50 cents or 55 cents each?
You posted both amounts.

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