TITLE: Nickels and dimes system of equations
QUESTION [7 upvotes]: John Cena has 20 coins consisting of nickels and dimes. If his nickels were dimes and his dimes were nickels he would have 70 cents more. How much are his coins worth?
so i did $$x+y=20$$
$$2x+y=70+x+y$$
$$x=70$$
$$y=-50 $$
but this obviously isnt the answer and i don't know what to do i need help

REPLY [4 votes]: If you don't like working with non-integers, you could "change units" and think of American currency in terms of nickels. However, until you're comfortable working with word problems (in particular being able to follow and replicate the "standard" approaches in the other answers), I suggest trying to follow the other answers first before trying to follow this one.
Viewing currency in units of nickels, we can say that if his nickels and dimes were interchanged, then the amount of additional money he would have is equivalent to 14 nickels. If $x$ and $y$ are the number of nickels and dimes he has, then $x+y=20$ (as you correctly stated), the total worth of his coins is $x+2y$ (since a nickel is worth $1$ nickel and a dime is worth $2$ nickels), while the total worth of his coins were they reversed would be $2x+y$. The last two bits of information combine to give
$$(2x+y) - (x+2y) = 14$$
which simplifies to
$$x - y = 14.$$
The system of equations
$$ x+y = 20 \\ x-y = 14 $$
yields $x = 17$ and $y = 3$, from which you can calculate that his total worth (in nickels!) is
$$ x + 2y = 17 + 2(3) = 23. $$
So you have the amount of money he owns, in nickels. Now convert that to dollars or cents by using the appropriate conversion.