How many of each type of bill does Garrett have?

Question

Garrett has $150 in ten & twenty-dollar bills. The number of ten-dollar bills in one less than twice the number of twenty-dollar bills. How many of each type of bill does Garrett have?

Answer 1

Let x = # $10 bills

Let y = # $20 bills

 

10x + 20y = 150      $150 in ten & twenty-dollar bills

x=2y-1                      Number of ten-dollar bills in one

                                 less than twice the number of twenty-dollar bills

 

 

We have 2 equations.  We can substitute 2y-1 in place of x

in the first equation to solve for y

 

10(2y-1)+20y=150

20y-10+20y=150

40y-10=150

40y=160

y=4

 

He has 4 of the $20 bills ... $80

He has 7 of the $10 bills ... $70

                                       ------

                                       $150

 

Answer 2

Hi Mackenzie!

The difficult part of this problem is setting up our algebraic equation:
We can start by expressing one of the unknowns, the number of twenty dollar bills as a variable, x.
Because we know the number of $10 bills is one less than twice the number of $20 bills, we can express it as: (2x-1)

Now we put it together in our equation and solve for x:
$150=$20(x)+$10(2x-1)
150=20x+20x-10

150=40x-10

160=40x

x=4

Because x=4, we know Garrett has 4 $20 bills. Now we plug x=4 into our equation for the number of $10 bills:
2x-1

2(4)-1

8-1

7

So Garrett must have 4 $20 bills and 7 $10 bills.

With these types of questions its always a good idea to check our answer to make sure it makes sense:
$150 = 4*($20) + 7*($10)

$150 = $80 + $70

$150 = $150