Daily Quiz Newsletter
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).† Itís 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 SELLERíS share of the sale price, NOT the brokerís share.† When you are subtracting the 7% commission, you are giving the seller 93% of the sale price (150,000 X 93%).† Thatís 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 canít 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.
Letís try some practice questions.
1.†† What does a house sell for if the seller receives $84,000 after paying a 6% commission?
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?
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?
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?
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?
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 Marilynís listings.† Marilynís broker pays the selling broker 55% of the 7% commission.† If Marilyn receives $3,515.40, what did the house sell for?
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 donít believe me, try it your way and then multiply YOUR sale price by 6% and subtract it from YOUR sale price.† If you donít get back to 84,000, you did it wrong.
2.†† $96,774.19.† REMEMBER, we canít 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% Ė 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 ų 93% = 96,774.19
3.†† $146,000.† MAKE SURE you put this in the right order.† Again, forward would be:
† Sale Price X 94% Ė 3000 Ė 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 ų 94% = 146,000.
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 canít 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
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 doesnít matter on this question, but you should get into that habit so you donít have figure when you need to do that and when you donít).† Going forward, we would have:† Sale Price X 7% X 55% X 53% = 2500,
so backwards we would use:
2500 ų 53% ų 55% ų 7% = 122,519
6.†† $180,000.† This is the same type of question, except one additional aspect has been thrown in.† Marilynís 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 ų 62% ų 45% ų 7% = 180,000