Melissa and Emily are playing at the pool. They have three different measuring jars for liters, cups, and pints. Melissa poured 7 cups of water and 3 liters of water into the pint jar and it was filled up to 9.8 pints. Later, Emily started with 5 liters of water in the pint jar and took out 9 cups. The remaining water level was equal to 6 pints.

Model the given situation as a system of linear equations and solve it for liters. Based on your solution, what do you notice about the relationship between pints and cups, and pints and liters?

Question

Melissa and Emily are playing at the pool. They have three different measuring jars for liters, cups, and pints. Melissa poured 7 cups of water and 3 liters of water into the pint jar and it was filled up to 9.8 pints. Later, Emily started with 5 liters of water in the pint jar and took out 9 cups. The remaining water level was equal to 6 pints.

Model the given situation as a system of linear equations and solve it for liters. Based on your solution, what do you notice about the relationship between pints and cups, and pints and liters?

Hero · Answer

Hi @dakotawalker welcome to QC. Were you able to start this one? If so, how far have you gotten with solving the system?

dakotawalker · Answer

hi hero. i have tried to start it but i don't really understand it.

Hero · Answer

Just a moment. Working on it.

Hero · Answer

Apparently the system is supposed to be
$\begin{align*}
7C + 3L &= 9.8P\
-9C + 5L &= 6P
\end{align*}$

Hero · Answer

In order to solve this, we have to eliminate one of the variables.

Hero · Answer

We have to solve for L so we can't eliminate that variable. We have to eliminate either C or P.

Hero · Answer

Are you still with me @dakotawalker

dakotawalker · Answer

yes please keep going

Hero · Answer

So I think it's easier to eliminate C. How do you suggest that we go about doing this?

dakotawalker · Answer

would combining them then subtracting work

Hero · Answer

Well, no, that's not how elimination works. We need to do something to each equation so that the coefficients of the C terms have opposite values. That way we can add the equations together to eliminate C

Hero · Answer

Any idea of what we can do to accomplish that?

dakotawalker · Answer

we need to make the c terms have the same numbers but be either positive or negative

Hero · Answer

And how would we go about doing that?

dakotawalker · Answer

we do seven times nine for both leaving one as a negative

Hero · Answer

The correct way to describe the process is to say: We multiply both sides of one equation by 7 and multiply both sides of the other equation by 9

Hero · Answer

And that process looks like this:
$\begin{align*}
9(7C + 3L) &= 9(9.8P)\
7(-9C + 5L) &= 7(6P)
\end{align*}$

Hero · Answer

Would you mind doing the next step?

dakotawalker · Answer

do we divide or do  make an equation

Hero · Answer

Are you familiar with the distributive property? a(b + c) = ab + ac. That's what we apply here. Also if you see a(b) it means multiply a and b.

dakotawalker · Answer

so it will be 9(9.8P+6P)= 9(9.8P)+9(6P)

Hero · Answer

Can you show me how you're applying the distributive property to arrive at this result?

Hero · Answer

I meant for you to apply the distributive property to this system:
$\begin{align*}
9(7C + 3L) &= 9(9.8P)\
7(-9C + 5L) &= 7(6P)
\end{align*}$

Hero · Answer

And we only apply it on the LHS. Are you familiar with the distributive property?

dakotawalker · Answer

A little but i have trouble with it and it has been a long time since i used it

Hero · Answer

I figured. You should review distributive property before continuing. I recommend YouTube and Khan Academy for reviewing and drilling on this concept.

dakotawalker · Answer

ok thank you but i have to go