Certainly! Let's solve the problem step by step.
1. Define the variables:
- Let [tex]\( g \)[/tex] be the number of girls.
- Let [tex]\( b \)[/tex] be the number of boys.
2. Set up the equations based on the information given in the problem:
- The total number of children is 65:
[tex]\[
g + b = 65
\][/tex]
- The total amount of money distributed is 2450, with each girl receiving 250 and each boy receiving 830:
[tex]\[
250g + 830b = 2450
\][/tex]
3. Substitute the value of [tex]\( b \)[/tex] from the first equation into the second equation:
- From [tex]\( g + b = 65 \)[/tex], we get [tex]\( b = 65 - g \)[/tex].
4. Formulate the equation by substituting [tex]\( b \)[/tex] in the total money equation:
[tex]\[
250g + 830(65 - g) = 2450
\][/tex]
5. Simplify the equation:
- Distribute 830 over [tex]\( (65 - g) \)[/tex]:
[tex]\[
250g + 830 \cdot 65 - 830g = 2450
\][/tex]
- Compute [tex]\( 830 \cdot 65 \)[/tex]:
[tex]\[
250g + 53950 - 830g = 2450
\][/tex]
6. Combine like terms and simplify further:
[tex]\[
250g - 830g + 53950 = 2450
\][/tex]
[tex]\[
-580g + 53950 = 2450
\][/tex]
7. Isolate the variable [tex]\( g \)[/tex]:
- Subtract 53950 from both sides of the equation:
[tex]\[
-580g = 2450 - 53950
\][/tex]
- Compute the subtraction:
[tex]\[
-580g = -51500
\][/tex]
8. Solve for [tex]\( g \)[/tex]:
- Divide both sides of the equation by -580:
[tex]\[
g = \frac{-51500}{-580}
\][/tex]
- Simplify the division:
[tex]\[
g = 88.79310344827586
\][/tex]
Therefore, the number of girls is approximately [tex]\( 88.79 \)[/tex].
Given the constraints of the problem and the solution steps, it shows the possibility of having fractional children, which suggests that there might be an issue or an error in the initial setup or premise. In practical situations, the interpretation might need a reassessment of the given values or conditions, as typically, the number of children should be a whole number.
