2/9of the people in a restaurant are adults. If there are 95 more children than adults, how many adults are there in the restaurant? How many children are there in the restaurant? Be sure to include a therefore statement; show your work for full marks. [
/4 marks]
Let x be the number of adults in the restaurant.
Since 2/9 of the people are adults, the number of children in the restaurant is (9/9 - 2/9) = 7/9 of the total number of people.
Given that there are 95 more children than adults, we can set up the following equation:
7/9 total people = x (number of adults) + x + 95 (number of children)
Now we can solve for x:
7/9 total people = 2x + 95
7/9 total people - 95 = 2x
2/9 total people = 2x
x = (2/9) * total people
x = (2/9) * (9/7) * (x + x + 95)
x = (2/7) * (2x + 95)
7x = 4x + 190
3x = 190
x = 190 / 3
x = 63.33 (rounded to the nearest whole number)
Therefore, there are 63 adults in the restaurant.
To find the number of children, we can simply substitute x back into the equation:
Number of children = 2x + 95
Number of children = 2 * 63 + 95
Number of children = 126 + 95
Number of children = 221
Therefore, there are 63 adults and 221 children in the restaurant.