# Algebra 1

#### sandyk109

##### New member
With the major options package and destination charge, a sports car cost $24,416. The base price of the car was ten times the price of the major options package and fifty times the destination charge. What was the base price of the car?$24,416 - x =10x + 50x
$24,416 -x = 60x + x$24,416 = 61X

This is not correct because the x on the left has to equal a dollar amount.

I just don't understand this one at all. Help!

#### nezenic

##### New member
I did this two ways and got the same answer both times. The number seems kind of steep at first, but when looking at the problem, it might seem correct after all.

Online Package + Destination Charge = 24,416 Dollars
Online Package * 50 = Base Price
Destination Charge * 10 = Base Prce

So Divide 50 and 10 Respectively and Substitute...

(1/50)Base Price + (1/10)Base Price = 24,416 Dollars.

Now just solve the equation for the Base Price. Use a variable and find the common denominator. Multiply that out, divide by co-efficient...

#### galactus

##### Super Moderator
Staff member
x=base price, y=options, z=destination charges.

$$\displaystyle \L\\x+y+z=24416$$

$$\displaystyle \L\\x=10y=50z$$

You could manipulate this in various ways. Pehaps,

$$\displaystyle \L\\y=5z$$

Which gives:

$$\displaystyle \L\\x+6z=24416$$

$$\displaystyle \L\\x=50z$$

$$\displaystyle \L\\50z+6z=24416$$

$$\displaystyle \L\\56z=24416$$

Find z, which is the destination charge. The rest will fall into place.

#### Denis

##### Senior Member
1/10 + 1/50 = 3/25

b = base price
b = 24416 - (3/25)b
(28/25)b = 24416

b = ?