System of equations

Question

Sam has only $10 bills and $20 bills in his wallet. He has 5 more twenties than tens if he has a total of $400 in his wallet, how many $10 bills does he have

Answer 1

If you have learned how to set up systems of equation word problems, here would be the process.

Assign values to the two different bills: Typically x and y for graphing purposes.

x represents $10 bill

y represents $20 bill

He has 5 more twenties than tens

y = x + 5 [all of the $10 plus 5 more bills is equivalent to the $20 bills]

He has a total of $400 in his wallet

10x + 20y = 400 [all of the $10 bills (x) times 10 since they have a monetary value of 10, plus all of the $20 bils (y) times 20 since they have a monetary value of 20, equals $400]

Now you can solve using substitution or by graphing the two equations and seeing where they intersect. The (x,y) coordinate of intersection will tell you the amount of x ($10 bills) and y ($20 bills).

Ordered pair (10,15)

If you use sbstitution you can plug [x+5] into the second equation to replace the y and solve for x.

10x + 20(x+5) = 400

When you're done you will get x = 10

Answer 2

For the SAT you should be able to do this mentally.

The "extra" $20 bills are $100.

That leaves $300 to be split evenly between the 10's and 20's.

10 of each!