A charity organisation sells greetings cards in packs costing $10 or $2.50 each. A total of 75 packs were sold at a fair for a total of $375. How many of the $2.50 packs were sold?

Question

mathstudent55 · Answer

This problem can solved with a system of equations.
First, we need two variables to represent the two unknown numbers.
Let x = the number of $10 packs.
Let y = the number of $2.50 packs.

mathstudent55 · Answer

We are told that 75 packs were sold.
Using our two variables, we know the number of packs sold is
$x + y$

This gives us our first equation:
$x + y = 75$

Do you follow so far?

anonymous · Answer

yes
I struggle when it comes to find the y

anonymous · Answer

You'll have a second equation: 10x + 2.5y = 375

anonymous · Answer

$10 for x packs, $2.50 for the y packs. Hopefully that makes sense.

mathstudent55 · Answer

Wait. We only wrote one equation so far.
The equation we wrote has two variables.
To find the values of two variables, we need two equations.
That equation dealt with the number of packs.
Now we need an equation that deals with the amount of money.

anonymous · Answer

375 is the amount of money that was received in the end.

mathstudent55 · Answer

If x number of $10 packs were sold, that was 10x dollars.
If y number of $2.50 packs were sold, that was 2.5y dollars.
We add the two amounts and we get
10x + 2.5y
We are told that $375 was the total amount of dollars sold, so that gives us the second equation

$10x + 2.5y = 375$

mathstudent55 · Answer

Now we have two equations in two unknowns. We can find the values of the variables.

mathstudent55 · Answer

This is the system of equations we need to solve to find the value of y, the number of $2.50 packs that were sold.

$\begin{cases} x + y = 75 \ 10x + 2.5y = 375 \end{cases}$

anonymous · Answer

I follow you! I was getting there but I can't understand the way it is solved after having these 2 equations. I can go as far as 10x=750-10y but then I dont know what to do with the 750
ty

mathstudent55 · Answer

We are solving for y, the number of $2.50 packs because that is all the problem asks for.
Let's solve the system by substitution.
We solve the first equation for x.

$x = 75 - y$

Now we replace x of the second equation with $\color{red}{75 - y}$.

$10\color{red}{x} + 2.5y = 375$

$10\color{red}{(75 - y)} + 2.5y = 375$

Distribute the 10.

$750 - 10y + 2.5y = 375$

Combine like terms on the left side.

$750 - 7.5 y = 375$

Subtract 750 from both sides.

$-7.5y = -375$

Divide both sides by -7.5

$y = 50$

Since y represents the number of $2.50 packs, the answer is:

The number of $2.50 packs sold is 50.

anonymous · Answer

God, only a misread of negativ...thanks so much for helping!

mathstudent55 · Answer

You're welcome.