The sum of ages of 22 boys and 24 girls is 160. What is the

Ans is C.
But I am sure that I am adopting the wrong method bcse time consuming

22x + 24y = 160
let's pick x+y=7
x=1; y=6 => 22+144 = 166
x=2; y=5 => 44+120 = 164
x=3; y=4 => 66+96 = 162
x=4; y=3 => 88+72 = 160
x=5; y=2 => 110+48 = 158
x=6; y=1 => 132+24 = 156

Basically what you can also notice is that if for (x+y)=7, you take the bigger possible factor (y) for 24 and the smallest, your result will be between 156 and 166

Basically what you can also notice is that if for (x+y)=5, you take the bigger possible factor (y) for 24 and the smallest, your result will be between 112 and 118

Basically what you can also notice is that if for (x+y)=6, you take the bigger possible factor (y) for 24 and the smallest, your result will be between 134 and 142

.....

Does that makes sense