Algebra word problem

Question

Last year, 250 people attended the year end celebration party. This year, the number of party- goers has skyrocketed. If the cost is 75 per 20 people, and your new budget is $1500, how many new people will be able to attend?

Answer 1

You can set up a proportion - if $75 pays for 20 people, how many people can attend for $1500?

One way to set up the proportion is $75/20 = $!500/x

Cross-multiply to solve: 75x = 30000, x = 400 people

Last year was 250, so there can be 150 more people this year.

Answer 2

Hi Margret,

First, we consider our initial 250 people, since our TOTAL budget is $1500. To get the cost for these people, compute:

250/20=12.5 This creates a 20-person "unit," so multiply this bty the cost per 20 people:

12.5*$75=937.50

So you spent $937.50 only on your initial 250 people. Now, let's see how much we have left:

1500-937.50=$562.50

Now, let's divide 562.50/75 to get the number of 20-person "units" we can afford.

562.50/75=7.5

Now, that's the number of 20-person "units," so we need to multiply by 20 to get the number of new people:

7.5*20=150

We can afford 150 new guests at the party.

I hope this helps.