Question 1193381
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First we will solve the problem using logical reasoning and simple mental arithmetic, since that gives us good mental exercise.<br>
If all 131 people were children, the total cost of admission would have been 131($7)=$917.
The actual cost, $1062, was $1062-$917 = $145 more.
The cost of each  adult admission is $5 more than the cost of each child admission.
The number of adult tickets, to make the additional $145, was $145/$5=29.<br>
ANSWER: there were 29 adults and 131-29=102 children<br>
CHECK: 29($12)+102($7)=$348+$714=$1062<br>
Using formal algebra....<br>
x = # of adults
131-x = # of children<br>
The total cost, at $12 per adult and $7 per child, was $1042:<br>
{{{12x+7(131-x)=1062}}}
{{{12x+917-7x=1062}}}
{{{5x=145}}}
{{{x=29}}}<br>
Adults: x = 29
Children: 131-x = 102<br>
Note that with this method of solving the problem using formal algebra, the calculations are exactly the same as with the informal method.<br>