A group of 48 people visits a museum. There were twice as many children as adults in the group. How do you write a system of equations you could solve to find the number of adults (a) and the number of children (c) in the group?

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Answer 1 · 2018-04-17T18:02:10

#{[2a=c],[a+c=48]:}#

There are twice as many children as adults, so #2a=c#. There were 48 children and adults total, so #a+c=48#.

Plugging the first equation into the second, #a+2a=48#, #3a=48#, #a=16# so there were 16 adults.

Plugging this into either equation gives #c=32# so there were 32 children.