Question

MEDAL WILL BE AWARDED. Please help. See attachment

Answer 1

@amistre64 @hartnn @ranga @AkashdeepDeb

Answer 2

Step #1 - Name Stuff.
Q1 - Name What?
A1 - What does it want? Name that.

G = Price of a stick of gum

Start traslating the problem statement.

Answer 3

Let \(x\) be the quantity of gum purchased, and \(y\) be the price of one piece. You have the system,
\[\begin{cases}xy=2.16\\
(x+3)(y-1)=2.16\end{cases}\]
Solve for \(x\).

Answer 4

How do I solve for x?

Answer 5

Substitution should work. From the first equation, you have \(y=\dfrac{2.16}{x}\). Expanding the second equation, you have
\[xy+3y-x-3=2.16\]
Plug in the expression for \(y\):
\[x\left(\frac{2.16}{x}\right)+3\left(\frac{2.16}{x}\right)-x-3=2.16\\
2.16+\frac{6.48}{x}-x-3=2.16\\
0=x+3-\frac{6.48}{x}\]

Answer 6

Is there any easier way than that please? I am not up to that level yet :)

Answer 7

It's a quadratic in disguise. Have you worked with quadratic equations?

Multiply both sides by \(x\):
\[0=x^2+3x-6.48\]

Answer 8

No

Answer 9

So you've never seen this formula before?
\[\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 10

no

Answer 11

Are you allowed to plot graphs and see where they intersect and find the solution that way?

Answer 12

well i dont know. i mean is there anything easier than a quadratic equation or something?

Answer 13

The $2.16 may have to be converted to pennies in the equations.

Answer 14

so that would be 216 pennies right?

Answer 15

Yes. You can write various factors of 216 and create a table and from there you may be able to find the answer.

Answer 16

any easier way than that?

Answer 17

Try out each answer choice. And you can eliminate the ones that don't work.