Question 1160642

Hello
How do I go about solving this problem?

There are 42 children in a canteen. 2/5 of the boys and 1/2 of the girls like to eat fried chicken wings. There are 19 children who like to eat fried chicken wings. Find the number of boys in the canteen.

Thanks in advance.
<pre>Let number of boys in canteen, be B
Then number of girls in canteen is: 42 - B
Number of boys who eat FCW: {{{matrix(1,3, (2/5) * B, or, 2B/5)}}}
Number of girls who eat FCW: {{{matrix(1,3, (1/2) * (42 - B), or, (42 - B)/2)}}}
Since 19 of the boys and girls in the canteen eat FCW, then we get: {{{matrix(1,3, 2B/5 + (42 - B)/2, "=", 19)}}} 
2(2B) + 5(42 - B) = 10(19) ------ Multiplying by LCD, 10
4B + 210 - 5B = 190 
4B - 5B = 190 - 210
- B = - 20
Number of boys in canteen, or {{{highlight_green(matrix(1,5, B, "=", (- 20)/(- 1), "=", 20))}}}