Question

Gigi offers two different packages of yoga classes at her yoga studio. She offers two normal yoga sessions and three zero gravity yoga sessions at a cost of $\$400$. She also offers four normal yoga sessions and two zero gravity sessions at a total cost of $\$440$. Gigi wants to offers a larger package for long-time clients in which, the cost must exceed $\$800$. If Gigi does not wish to include more than $13$ sessions for the long-time client package, will she be able to create this package for her clients?

• A. No, because the closest package that she can offer consists of three normal yoga and three zero gravity yoga sessions.
• B. No, because the closest package that she can offer consists of four normal yoga and four zero gravity yoga sessions.
• C. Yes, because she can offer five normal yoga and five zero gravity yoga sessions.
• D. Yes, because she can offer six normal yoga and six zero gravity yoga sessions.

Answer 1

Answer: (D)

Yes, because she can offer six normal yoga and six zero gravity yoga sessions.

Let the Giri cost for normal yoga is $\$x$ and $\$y$ for zero gravity yoga session

Then first package $2x+3y=400$.....(1)

And for second package $4x+2y=440$.....(2)

Multiply equation (1) by $2$, we get

$4x+6y=800$.......(3)

Subtract equation (2) with (3), we get

$4y=360$

$\therefore y=90$

Put the value $y=90$ in equation (1), we get

$2x+3\times 90=400$

$\Rightarrow 2x+270=400$

$\Rightarrow 2x=130$

$\Rightarrow x=65$

Then for $5$ normal and $5$ zero gravity sessions cost $=450+325=\$775$ this is not exceed $\$800$.

Then for $6$ normal and $6$ zero gravity sessions cost $=540+390=\$930$ this exceeds $\$800$.

Yes, because she can offer six hot yoga and six zero gravity yoga sessions.