I need help with this one math problem.

Question

A refrigerator repairman bought some replacement condenser units for a total of $360. If the cost per unit could have been $6 less, he could have bought 2 more units. How many units was he able to buy?

A. 13 units

B. 12 units

C. 10 units

D. 9 units

Answer 1

The answer is c. 10

-The process-

x = number of units bought

u = price of each unit ($)

We know that x*u=$360

Sadly we don't know how many units (x) or the price per unit (u)

However, we know that:

(u-6)(x+2)=$360

If every unit (u) cost $6 less [u-6] then he could have bought 2 additional units [x+2] for $360

Here I will guess and check using the answer choices

I like to start with the lowest number to see how close that is. It helps me determine which one to try next if it isn't correct.

(u-6)(x+2)=360

--------------------substitute 9----------------------------

(u-6)(9+2)=360

-------------------add 9+2---------------------------------

(u-2)11=360

-----------------divide both sides by 11---------------------

(u-2)=32.727

----------------add 2 to both sides------------------

u=34.727

You can't buy 0.727 of a unit, so I am going to say that 9 is not correct.

Next I'll try 10

(u-6)(x+2)=360

--------------------substitute 10----------------------------

(u-6)(10+2)=360

------------------add 10+2------------------------

(u-6)12=360

------------------divide both sides by 12--------------

u-6=30

------------------add 6 to both sides---------------

u=36

As this is a whole number, I'll accept it.

Now to check

xu=$360

10*36=360

The answer is c. 10