2/9 of the people in a restaurant are adults. If there are 95 more children than adults, how many children are there in the restaurant?

Answer 1

You must use three equations. The first one represents the ratio of adults to the total people present.

Let t=total people in room

And a = total adults

The first equation is: 2/9 = a/t

The second equation represents the total people in the room

Let c = the number of children

The second equation is: t = a + c

The third equation relates adults to children: c=95+a

First substitute the t in the first equation for t in the second.

2/9=a/(a+c)

Rearrange the third equation to solve for a and get: c-95=a

Subtitute a into the previous equation to get

2/9=(c-95)/(c-95+c) simplifies to 2/9=(c-95)/(2c-95)

Multiply both sides by 9(2c-95)

2(2c-95)=9(c-95)

Distibute the 2 and the 9

4c-190=9c-855

Simplify

655=5c

Solve for c

C = 131

The number of children in the room is 131