A theater sells adult tickets for 12 and child tickets for 7. If 150 tickets were sold for a total of $1,425, how many adult tickets were…

Let $a$ be adult tickets and $c$ child tickets. Then $a+c=150$ and $12a+7c=1425$. Substitute $c=150-a$: $12a+7(150-a)=1425$, so $5a+1050=1425$ and $5a=375$, giving $a=75$, choice J. Check: $75$ adult tickets bring in $900 and $75$ child tickets bring in $525, for a total of $1,425. Choice F ($65$) yields $1,375. Choice H ($85$) yields $1,475. Choice G ($100$) yields $1,550. Only $75$ gives the stated total with $150$ tickets. Always check the totals for both the number of tickets and the revenue.