word problem

Question

A group of people agree to share the cost of a 15000 repair bill to an inn.Before the repairs are made,two more people join the group and enter the agreement.As a result,each person's share is reduced by $250.How many people were in the original group?

Answer 1

Hi Weminobs!

This is a perfect example of a problem solving strategy that I call "think logically before mathematically". For this problem, think about how you would calculate the cost per person if you knew how many people there were. For example if there were 10 people in the group the cost per person would be 15000/10=1500. But we do not know how many people there were and we do not know what the cost per person was before the two new people joined. Lets call the number of original people x and the original cost per person y. Then try to put the problem into mathematical terms. The first sentence would translate into, 15000/x=y because they would take the cost and divide it by the number of people to get the cost per person. Now the next sentence, mentions 2 new people who join the group, so now instead of x number of people we have x+2 and as a result the cost per person decreases by 250, so that in an equation looks like: 15000/(x+2) = y-250. Now to solve this problem we can use substitution or elimination. I think substitution would be easier since the first equation is already solved for one of the variables. So if we substitute 15000/x for y in the second equation we get: 15000/(x+2) = 15000/x -250. If we multiply by the entire equation by the common denominator which is x(x+2) we get: 15000x=15000(x+2) -250x(x+2). Now simplify and solve for x. Hope that helps!

 

Answer 2

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