# Real life word problem

#### jonesmatty

##### New member
We are trying to calculate how much each adult and each kid should pay for a stay at a house. We are looking for the equation, not the answer.
The price of the house will be $8000. Each kid will pay 1/2 as much as the adults. There are 16 adults and 14 kids. Average cost = p/(a+(k/2)) Having trouble backing out price per adult and price per kid. #### lev888 ##### Senior Member We are trying to calculate how much each adult and each kid should pay for a stay at a house. We are looking for the equation, not the answer. The price of the house will be$8000. Each kid will pay 1/2 as much as the adults. There are 16 adults and 14 kids.

Average cost = p/(a+(k/2))

Having trouble backing out price per adult and price per kid.
Don't understand neither why you need the average cost nor the expression.
The equation:
8000=total adult cost + total kid cost
Can you complete it?

#### JeffM

##### Elite Member
$$\displaystyle 16a + 14k = 8000 \text { and } k = \frac{1}{2} * a.$$

Solve that system of equations to figure out what is due for each adult and each kid.

What that average you asked about is supposed to tell you is beyond me.

#### Jomo

##### Elite Member
16 + 14/2 = 23. \$8000/23 = what each adult pays.

That must be one big house!

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#### nasi112

##### Full Member
$$\displaystyle 14x + 16 \cdot 2x = 8000$$

where $$\displaystyle x$$ is the price that one kid will pay