Linear equation word problem

Question

how much money did a man have if he had $240 left after spending 20% of it at one store and 30% of it at another store ?

Answer 1

Alex,

 

Let m represent the amount of money the man started with.  Then he spent 20% of m (.2m) at one store and 30% (.3m) at the second (assuming the 30% is taken from the original starting amount and not what he had left after spending 20%).

 

Then:

 

$240 = m - .2m - .3m

 

$240 = s - .5m

 

$240 = .5m

 

$480 = m (the amount he started with)

 

If the assumption I mentioned does not hold, and the 30% is taken from what's left after spending the first 20%, then the equation would look like this:

 

$240 = m - .2m - .3(m - .2m)

 

You can solve the equation using distribution and combining like terms.

 

Make sense?

Answer 2

Alex, we are going to make some assumptions here. The problem doesn't directly state that he spend 20% and 30% of the ORIGINAL price at each place, but we'll assume that's what the problem tells us.

 

If he spent 20% and then 30%, then he spent 50%, right? This means that the $240 is the other 50%, or half. $240 is half of $480, so that's how much he had to start with.

 

The problem would be different if he spent 20% at one store and 30% of the remainder, but, again, we're going to assume both are percentages of what he started with.