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College Algebra Word Problem


label Algebra
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A number of students rented a car for $320 for a one-week trip. If eight more students had joined the original group, each person's share of expenses would have been reduced by $20. Use algebraic equations to find out that how many students were in the original group?

Nov 19th, 2017

The cost of the rental car is fixed (it will always be $320).

The cost is equal to the number of students multiplied by the cost per student.

Let the number of students equal n and the cost per student be c.

Therefore in the original group:

n*c = 320

When they add 8 more students the total number is n + 8 and the cost become c - 20.

In the second situation,

(n + 8)(c - 20) = 320

FOIL the equation above.

nc + 8c - 20 n - 160 = 320

We can use the first equation to isolate a variable, so that 

c = 320 / n

Now, plug that value into the FOILed version of the second equation:

n* 320 / n + 8*320 / n - 20n - 160 = 320

320 + 2560 / n - 20 n - 160 = 320

2560 / n - 20 n - 160 = 0

Multiply the entire equation by n

-20n^2 - 160 n + 2560 = 0

Solve for n :

-20 ( n^2 + 8n - 128 ) = 0

-20 ( n + 16 ) (n - 8) = 0

n = -16

n = 8

The solution would be n = 8 because a negative number of people is not logical.

There were 8 students in the original group.

Apr 6th, 2015

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