Question

There are xboys playing in the park. The number of girls playing in the park is equal to the square root of the number of boys. If the total
number of boys and girls playing in the park is 42, find the number of boys.
A. 49
B.6
C. 36
D. 7

Answer 1

Answer:

x = 36 and √x = 6; total 42 children

Step-by-step explanation:

Number of boys:  x

Number of girls:  √x

Total number of kids:  x + √x = 42.

Find x.

Rewrite x + √x = 42 as √x = 42 - x.  Then square both sides:

x = 1764 - 84x + x^2, or

x^2 - 85x + 1764 = 0

Check out Answer C:  x = 36.  Is the above equation true for x = 36?  YES

Check out Answer A:  x = 49.  Is the above equation true for x = 49?  YES

Assume that x = 36.  This would be the number of boys.  The number of girls would be √36, or 6.  Does the sum of 36 and 6 equal 42?  YES.  So the number of boys is 36 and the number of girls is 6.

Assume that x = 49.  This would be the number of boys.  The number of girls would be √49, or 8.  Does the sum of 49 and 7 equal 42?  NO.  So we reject x = 49 as the number of boys and accept x = 36 as being correct.