Final answer:
To find the total number of children at the art show, divide the total number of children by 4 to find the number of girls. Then rearrange the equation to isolate the number of girls and substitute the given information about the number of boys to solve for the total number of children. Finally, divide both sides of the equation by 3 to find the total number of children is 49.
Step-by-step explanation:
To find the total number of children at the art show, we need to determine the number of girls and boys. We are told that one out of every 4 children is a girl, and there are 21 boys. Let's calculate the number of girls first.
Since one out of every 4 children is a girl, we can divide the total number of children by 4 to find the number of girls:
Total number of children = Number of girls + Number of boys
Girls = Total number of children / 4 = (21 + Number of girls) / 4
Then, we can rearrange the equation to isolate the Number of girls:
Number of girls = (Total number of children - 21) / 4
Now, we can substitute the given information about the number of boys and solve for the Total number of children:
Total number of children = (Number of girls + 21) + 21 = (21 + (Total number of children - 21) / 4) + 21
Multiplying both sides of the equation by 4 to eliminate the fraction:
4 * Total number of children = 84 + Total number of children - 21 + 84
Combining like terms:
3 * Total number of children = 147
Dividing both sides of the equation by 3:
Total number of children = 4
Therefore, the total number of children at the art show is 49.