Sara has $50 in her wallet in $5 and $20 bills. Create a linear equation (with appropriate variables) and determine all of the possible combinations that she could
have.

0 $20 bills and 10 $5 bills

1 $20 bills and 6 $5 bills

2 $20 bills and 2 $5 bills

Step-by-step explanation:

Equations

Let's set:

x=number of $5 bills

y=number of $20 bills

The total amount Sara has is given by

5x+20y

And we know it's equal to $50, thus:

5x+20y=50

Dividing by 5

x+4y=10

We would need another condition to solve for x and y, but we can determine some combinations that solve the problem.

Solving for x:

x=10-4y

Since both x and y are integers and cannot be negative:

10-4y≥0

Swapping sides:

4y≤10

Dividing by 4:

y≤2.5

Thus, y can only have the values {0,1,2}

For y=0

x=10-4*0=10

x=10

For y=1

x=10-4*1=6

x=6

For y=2

x=10-4*2=2

x=2

Thus, the possible combinations are:

0 $20 bills and 10 $5 bills

1 $20 bills and 6 $5 bills

2 $20 bills and 2 $5 bills

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