Question 1090467
<br>"James to receive $2 000 less than the total of Jacob and Joshua to receive 5 times as much as Jacob."<br>
<br>That statement does not make sense grammatically; there is no way to interpret it in a meaningful way.  I can make sense out of "James to receive $2 000 less than the total of Jacob and Joshua"; but then the rest of the sentence has no meaning.<br>
Take a look at it and see if you didn't leave something out, or in some other way not present the information correctly.<br>
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Thanks for the clarification.  I suspected that was what you were trying to say, but I wasn't sure.<br>
So the amount James gets is 2000 less than the total the Jacob and Joshua get, and Joshua gets 5 times as much as Jacob.<br>
A formal algebraic solution might look like this:
let x = amount Jacob gets
then 5x = amount Joshua gets
then 6x - 2000 = amount James gets<br>
The total is 60,000, so
{{{x+5x+6x-2000=60000}}}
{{{12x-2000=60000}}}
{{{12x = 62000}}}
{{{x = 5166.67}}}<br>
Having that amount turn out to be not a whole number is not pleasant....<br>
So the amounts each gets are
Jacob: x = $5166.67
Joshua: 5x = $25833.33
James: 6x-2000 = $29000<br>
<br>An informal solution is probably easier than that, especially since our value for x in the algebraic solution turned out not to be a whole number.<br>
James is to get $2000 less than the total that Jacob and Joshua get.  If he got exactly the same as the other two together, he would get $30000 and they together would get $30000.  But since he is to get $2000 less than the other two together, the $60000 would be divided with $29000 going to James and $31000 to the other two.<br>
So we already know the amount that James gets; then to finish the problem we just need to divide the $31000 that Jacob and Joshua get in such a way that Joshua gets 5 times as much as Jacob.<br>
Since Joshua gets 5 times as much as Jacob, the ratio is 5:1, which means Jacob gets 1/6 of the $31000, which is $5166.67, and Joshua gets the rest of the $31000, which is $25833.33.