Supply Trading for Teachers

Question

Three teachers got in a discussion to trade teaching supplies. Here's their conversation.

Kyle to Brian: I'll give you 14 autographs of Harry for a sharpee, then you'll have three times as many supplies as I

Brian to Mason: I'll give you six erasers for a sharpee, then you'll have twice as many supplies as I do

Mason to Kyle: I'll give you four pencils for a sharpee, then you'll have six times as much as me

Harry to Kyle, Brian, and Mason: Here's five dollars, go and buy what you need and don't forget your coupons.

How many school supply items did each have? The autograph is a school supply.

Answer 1

The first step to solving this problem is to assign variables:

K = Kyle

B = Brian

M = Mason

H = Harry

SH = Sharpee

E = Erasers

S = Autographs (School Supply)

P = Pencils

Sh = Sharpee

Then with the given information and relationships with each of our defined variables we can create equations:

Sh = 14 * S

Sh = 6 * E

We can further substitute 14*S into Sh:

14 * S = 6 * E

E = (14*S)/6

Sh = 4 * P

We can further substitute 14*S into Sh:

14 * S = 4 * P

P = (14*S)/4

B = 3 * K

M = 2 * B

K = 6 * M

B = 6 * E = 14 * S

So, Brian has 14 Supplies as S = Autographs and Autographs are supplies.

Then we can substitute 14 * S into M = 2 * B:

M = 2 * (14*S) = 28 * S

Mason has 28 Supplies therefore

K = 6 * M = 6 * (28 * S) = 168 * S

Kyle has 168 Supplies therefore

Then we add the total amount of supplies for the final answer:

14 + 28 + 168 = 210 supplies

Therefore, 210 supplies is the final answer.