*Your
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**WORKING
MATH PROBLEMS BACKWARDS**

Not every math problem that you
will ever run across is straightforward (I realize there is a look of disbelief
going over your face right now). It’s
easy enough to take a $150,000 sale price, subtract a 7% commission, and then
subtract $4,000 in additional closing costs to get a $135,500 net for the
seller. But suppose you were told that
the seller nets $135,500 and had to find the sale price, how would you do
it? Would you take 7% of the 135,500? Would you add the 4,000 on and then take
7%? Do you deal with the commission
first or last? You have to handle this
by working backwards. First, pay
attention to the fact that going forward, you were worried about the SELLER’S
share of the sale price, NOT the broker’s share. When you are subtracting the 7% commission, you are giving the
seller 93% of the sale price (150,000 X 93%).
That’s what you did FIRST. THEN
you subtracted the $4,000. When we go
backwards, we do everything the opposite, and we MUST go in the reverse
order. The LAST thing we did going
forward was SUBTRACT 4000, so the FIRST thing we have to do going backwards is
ADD the 4000 back in. The FIRST thing
we did was MULTIPLY by 93%, so going backwards the LAST thing we have to do is
DIVIDE by 93% to get 150,000. If you do
this any other way, you will get the wrong answer.

Also be prepared for the
possibility that questions will not be worded in the order that things
happen. Make sure you put it in the
right order when you are answering the question. Use logic. If you are
looking at what a salesperson gets paid, you can’t pay the salesperson before
you pay their broker. When figuring
what the seller gets, remember that the commission is always the first thing
taken out when going forwards, and the last thing you would deal with going
backwards.

Let’s try some practice
questions.

1. What does a
house sell for if the seller receives $84,000 after paying a 6% commission?

**DO the problem, and click here to see if
you are right**

2. A seller
must pay a 7% commission and $4,500 in closing costs. If they receive $85,500 at settlement, what was the sales price
of the house?

**DO the problem, and click here to see if
you are right**

3. If a seller
nets $91,240 after paying $3,000 in miscellaneous closing costs, a 6%
commission, and paying off a $43,000 mortgage, what did their house sell for?

**DO the problem, and click here to see if
you are right**

4. Anna Belle,
a salesperson at Starfish Realty, receives 55% of all commissions she brings
into her company. If she sells a house
for $240,000, and her company gets 60% of the 8% commission, how much did she
get paid?

**DO the problem, and click here to see if
you are right**

5. A
salesperson receives 53% of all commissions he brings into his company. His company receives 55% of the commission
on a house that he sells. If the seller
is paying a 7% commission, what did the house sell for if the salesperson
receives $2,500?

**DO the problem, and click here to see if
you are right**

6. Marilyn, a
salesperson at Seahorse Realty, is paid 62% of any commission she brings into
her company. A salesperson from another
company sells one of Marilyn’s listings.
Marilyn’s broker pays the selling broker 55% of the 7% commission. If Marilyn receives $3,515.40, what did the
house sell for?

**DO the problem, and click here to see if
you are right**

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*ANSWER*

1. $89,361.70. If the broker receives a 6% of the sale
price, then the seller receives 94%. It
has to add up to exactly 100%, so the entire sale price is accounted for. The sale price times 6% percent would tell
us the amount the broker would receive, therefore, the sale price times 94%
would tell us what the seller receives, which we know is $84,000. When we go backwards, we do the opposite, so
84,000 DIVIDED BY 94% will give you the answer, which is $89,361.70. If you don’t believe me, try it your way and
then multiply YOUR sale price by 6% and subtract it from YOUR sale price. If you don’t get back to 84,000, you did it
wrong.

*ANSWER*

2. $96,774.19. REMEMBER, we can’t change the order. We have to do everything exactly in reverse,
and do the exact opposite of what we did going forward. And again, remember that if there is a 7%
commission, the seller gets 93%. Going
forward we would use: Sale Price X 93%
– 4,500 = 85,500. Going backwards, we
would start at the 85,500, THEN add the 4,500 back in, and AFTER THAT, divide
by 93%, so our equation would be: 85,500 + 4,500 ÷ 93% = 96,774.19

*ANSWER*

3. $146,000. MAKE SURE you put this in the right
order. Again, forward would be:

Sale Price X 94% – 3000 – 43,000 = 91,240,
so backwards we would start at 91,240, add the 43,000 and the 3,000 back in,
and then divide by 94% giving us: 91,240 + 43,000 + 3,000 ÷ 94% = 146,000.

*ANSWER*

4. $6,336. This question is going forward, so you can
see how it works. Put it in the right
order first. We start at the sale
price, then the total commission is paid (the salesperson can’t get paid before
the broker does). After the total
commission is paid, then it is split between the brokers (that also has to
happen before the salesperson is paid).
THEN the salesperson gets their share.
So this would give us: 240,000 X
8% X 60% X 55% = 6,336

*ANSWER*

5. $122,519. This is the same thing only backwards. Notice above we multiplied at every step, so
going backwards we would divide at every step.
And again, we should put in the right order (it actually doesn’t matter
on this question, but you should get into that habit so you don’t have figure
when you need to do that and when you don’t).
Going forward, we would have:
Sale Price X 7% X 55% X 53% = 2500,

so
backwards we would use:

2500 ÷ 53% ÷ 55% ÷ 7% = 122,519

*ANSWER*

6. $180,000. This is the same type of question, except
one additional aspect has been thrown in.
Marilyn’s broker paid the selling broker 55%. That means that her broker KEPT 45%, which is what we would use. Going forward, we would have: Sale Price X 7% X 45% X 62% = 3515.40,

so backwards
we would use:

3,515.40
÷ 62% ÷ 45% ÷ 7% = 180,000

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