Theresa has $26 in her wallet. The bills are worth either $5 or $1. If there are 14 bills total, how many does she have of each type?

Is it 3 fives and 11 ones

Set up your given:

Let x be $5
Let y be $1
Amount: 5x + y = 26
Number of bills: x + y = 14

Solve the equations by elimination:
(multiply the first equation by -1 to make y negative.. it would then cancel out)
-5x - y = -26
x + y = 14
-4x = -12
x = 3

Plug in x to any of your orig. equations
x + y = 14
$5 = 3
$1 = 14-3
= 11

Check: 3 $5 bills and 11 $1 bills equal to 14 bills.
Check: 3x$5 = $15
11x$1 = $11
$15 + $ 11 = $26

Let's assume Theresa has x bills worth $5 and y bills worth $1.

Based on the given information, we can form the following equations:

1. The total value of the bills equals the total amount Theresa has, which is $26:
5x + 1y = 26

2. The total number of bills is 14:
x + y = 14

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the method of substitution:

1. Rearrange equation 2 to express y in terms of x:
y = 14 - x

2. Substitute this value for y in equation 1:
5x + 1(14 - x) = 26

3. Simplify the equation:
5x + 14 - x = 26
4x + 14 = 26

4. Move 14 to the other side of the equation:
4x = 26 - 14
4x = 12

5. Divide both sides of the equation by 4:
x = 12 / 4
x = 3

Now that we know x = 3, we can substitute this value back into equation 2 to find y:

y = 14 - x
y = 14 - 3
y = 11

Therefore, Theresa has 3 bills worth $5 (x = 3) and 11 bills worth $1 (y = 11).

To find out how many bills of each type Theresa has, we can set up a system of equations. Let's say she has x bills worth $5 and y bills worth $1.

Given that there are 14 bills total, the first equation we can write is:
x + y = 14

Given that the total value of the bills is $26, the second equation we can write is:
5x + 1y = 26

To solve this system of equations, we can use the method of substitution.

From the first equation, we can rewrite it as:
x = 14 - y

Substituting this value of x into the second equation, we get:
5(14 - y) + 1y = 26

Expanding and simplifying, we have:
70 - 5y + y = 26
70 - 4y = 26

Moving the variables to one side, we get:
-4y = 26 - 70
-4y = -44

Dividing both sides by -4, we find:
y = -44 / -4
y = 11

Now that we have the value of y, we can substitute it back into the first equation to find x:
x + 11 = 14
x = 14 - 11
x = 3

Therefore, Theresa has 3 bills worth $5 and 11 bills worth $1.