Question

(If you can answer this, you're smarter than a fifth grader) Sam bought 300 pens and highlighters for $370. He sold the pens at three for $7 and the highlighters at four for $5. He made $135 for selling all the pens and highlighters. How many pens did Sam buy?

Answer 1

This is just a mixure problem.

Answer 2

Yes, give me the medal because you know I'm getting closer to the answer

Answer 3

Yeah, thanks, I think I could take it from here

Answer 4

And hey, look at that, you're smarter than a fifth graderrrr

Answer 5

Geez, it took long enough for this to come back. I was about to correct a solution I posted, but OS went completely off the grid. Geez...

Anyways, here's the correct solution finally figured it out. Nobody else was bold enough to attempt it

p + h = 300

7p/3 + 5h/4 = 370 + 135 = 505

28p/12 + 15h/12 = 505

(28p + 15h)/12 = 505

28p + 15h = 505*12

28p + 15h = 6060

p = (6060 - 15h)/28

p = 300 - h

p = p

28(300 - h) = 6060 - 15h

8400 - 28h = 6060 - 15h

8400 - 6060 = 28h - 15h

2340 = 13h

h = 180
p = 220

Answer 6

I also had the same solution but the openstudy.com site went down and couldn't post it. This was one of the toughest to set up that I have encountered on this site.

Congratulations Hero, you got there first.

Answer 7

Yeah, you had to figure out that the 135 was a profit. I agree. It was tough. That was the only part I didn't figure out until later. But I was getting there.

Answer 8

I was going to post the following:

Solve the following for p and h:\[\left\{p+h=300,\frac{7}{3}p+\frac{5}{4}h=505\right\}\]\[\{p=120,h=180\} \]

Answer 9

Oops

Answer 10

I subtracted wrong and put 220 instead of 120

Answer 11

I hate when I make it all the way to the end, then post a mistake.

Answer 12

I know you probably check your answers before you post them. Me, I'm kinda sloppy. But at least the other person knows I am working on the problem.

Answer 13

I use Mathematica for the calculations, so if the input is correct, the output is as good as gold. Did loose a lot time when I was trying to solve with
. . .= 500 rather than the correct . . .= 505. Kept getting crazy fractions which indicated a mistake in algebraic formulations.

Got to break off. It's almost midnight here in Santa Cruz, CA.

Answer 14

I'm in IA so it's even later