An art teacher has a jar containing b buttons to distribute to her class for a project .In order to give each children in the class 6 buttons , she will need 18 more buttons. If she gives each children 5 buttons,she will hav 4 left over.How many children are in the class?

Options

A. `17`
B. `19`
C. `22`
D. `24`

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the Variables
Let \( C \) be the number of children in the class. The number of buttons the teacher has is denoted by \( B \).

### Step 2: Set Up the First Equation
According to the problem, if the teacher gives each child 6 buttons, she will need 18 more buttons. This can be expressed as:
\[ B = 6C - 18 \]
This equation states that the total number of buttons \( B \) is equal to the number of buttons needed for all children (6 buttons each) minus the shortage of 18 buttons.

### Step 3: Set Up the Second Equation
If the teacher gives each child 5 buttons, she will have 4 buttons left over. This can be expressed as:
\[ B = 5C + 4 \]
This equation states that the total number of buttons \( B \) is equal to the number of buttons given to all children (5 buttons each) plus the 4 buttons left over.

### Step 4: Set the Equations Equal to Each Other
Since both equations represent the same total number of buttons \( B \), we can set them equal to each other:
\[ 6C - 18 = 5C + 4 \]

### Step 5: Solve for \( C \)
To solve for \( C \), we first subtract \( 5C \) from both sides:
\[ 6C - 5C - 18 = 4 \]
This simplifies to:
\[ C - 18 = 4 \]
Next, we add 18 to both sides:
\[ C = 4 + 18 \]
Thus, we find:
\[ C = 22 \]

### Step 6: Conclusion
The number of children in the class is \( C = 22 \).

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