Two Different Word Probs: Two consecutive numbers & how many students went on trip

[markl77]

Two Different Word Probs: Two consecutive numbers & how many students went on trip

The first word problem says :

Two consecutive numbers are represented by (x) and (x+1). If 6 is added to the first number and two is subtracted from the second number, the quotient of the new numbers is (9/2). Determine the numbers algebraically.

Here is my work
x, (x+1)
1/[(6+x)(x-2)] = (9/2)
2 = 9[(x+6)(x-2)]
=9x^2+36x-110

But when I factor this, I just get horrible numbers that cant be the numbers for the equation. The problem I have is setting it up, I have no idea how to do that and the textbook offers no help.

The second word problem says :
A club collected the same amount from each student going on a trip. When six students could not go, each of the remaining students were charged an extra 3$. If the total cost was $540, how many students went on the trip?

540 = 1/x + 1/(x+3)
540x+1620=x+3+x
538x=-1617
which gives me a negative number of course...

 

[mmm4444bot]

Two consecutive numbers are represented by (x) and (x+1). If 6 is added to the first number and two is subtracted from the second number, the quotient of the new numbers is (9/2). Determine the numbers algebraically.

Here is my work
x, (x+1)
1/[(6+x)(x-2)] = (9/2)

In the future, please start a separate thread for each exercise. (Please read the forum guidelines).

There are two things that need fixing.

x-2 is not correct; you subtracted 2 from the first number instead of from the second number.

The quotient of two numbers is the ratio:

(First Number) / (Second Number)

Instead, you set up the reciprocal of the product of the two numbers.

Fix these issues, and you're good to go. :cool:

The second word problem says :
A club collected the same amount from each student going on a trip. When six students could not go, each of the remaining students were charged an extra 3$. If the total cost was $540, how many students went on the trip?

540 = 1/x + 1/(x+3)
540x+1620=x+3+x
538x=-1617

I'm not following your steps. There are two unknowns, in this exercise, so let's write a system of two equations.

Let x = the number of students

Let a = the amount each student is charged

Write two equations, using the relationship:

(Amount Charged) times (Number of Students) equals (Total Cost)

We just picked symbols for the amount charged and the number of students; the total cost is given.

Write the equation.

Using the same relationship, write the second equation (i.e., when 6 fewer students go, the amount charged increases by 3).

Solve the system.

Please show your work, if you need more help on these exercises.