# Thread: Constructing simultaneous Equations

1. ## Constructing simultaneous Equations

I'm trying to work this sum out,

A party was organized for thirty people at which they could have either a hamburger or a pizza. If there were five times as many hamburgers as pizzas calculate the number of each.

I've been trying to work out and answer for over half an hour now but so far I could only come up with

$x =$ number of pizzas
$y =$ number of hamburgers

Equation 1 :
$x+y=30$

Equation 2:
$5x-y=0$

Is this correct?

2. Originally Posted by 22upon7
I'm trying to work this sum out,

A party was organized for thirty people at which they could have either a hamburger or a pizza. If there were five times as many hamburgers as pizzas calculate the number of each.

I've been trying to work out and answer for over half an hour now but so far I could only come up with

$x =$ number of pizzas
$5x =$ number of hamburgers

But that's obviously not right. I can't seem to find a value for $y$ or a way to construct the simultaneous equation.
You shouldn't use x to stand for both pizzas AND hamburgers.

Let x be number if hamburgers and y be number of pizzas.

There are 30 people in total, and they only have one, so the total number of hamburgers PLUS pizzas is 30.

$x + y = 30$

And, as stated, there are 5 times as many hamburgers as pizzas, so:

$x = 5y$

3. Hello, 22upon7!

so I assume we want to construct a system of equations.

A party was organized for thirty people at which they could have either a hamburger or a pizza.
If there were five times as many hamburgers as pizzas calculate the number of each.

Let $H$ = number of hamburgers.
Let $P$ = number of pizzas.

Then we have: . $\begin {array}{c}H + P \:=\:30 \\ H \:=\:5P \end{array}$

Now solve the system: . $\begin{array}{ccc}H + P &=& 30 \\ H - 5P &=& 0\end{array}$ . by your favorite method.

4. Originally Posted by Mush
You shouldn't use x to stand for both pizzas AND hamburgers.

Let x be number if pizzas and y be number of hamburgers.

There are 30 people in total, and they only have one, so the total number of hamburgers PLUS pizzas is 30.

$x + y = 30$

And, as stated, there are 5 times as many hamburgers as pizzas, so:

$x = 5y$
Thanks for that I just worked the sum a but more and got it, your answer confirms it. Thanks again!

5. Originally Posted by Soroban
Hello, 22upon7!

so I assume we want to construct a system of equations.

Let $H$ = number of hamburgers.
Let $P$ = number of pizzas.

Then we have: . $\begin {array}{c}H + P \:=\:30 \\ H \:=\:5P \end{array}$

Now solve the system: . $\begin{array}{ccc}H + P &=& 30 \\ H - 5P &=& 0\end{array}$ . by your favorite method.

Thanks