Yesterday, Ernest's Doughnut Shop sold 5/6 as many chocolate doughnuts as cinnamon doughnuts. If they sold 8 trays of cinnamon doughnuts, how many trays of chocolate doughnuts did they sell?

Question

Yesterday, Ernest's Doughnut Shop sold 5/6 as many chocolate doughnuts as cinnamon doughnuts. If they sold 8 trays of cinnamon doughnuts, how many trays of chocolate doughnuts did they sell?

Answer 1

Hi there!

For this problem, we are trying to solve for an unknown, chocolate doughnuts. Therefore, it makes the most sense to represent are unknown with a variable, x, in an algebraic equation.

Since 5/6 as many chocolate doughnuts as cinnamon doughnuts were sold, the ratio of chocolate doughnuts to cinnamon doughnuts is 5:6, which can be represented in an equation as:

6*(# of chocolate doughnuts)=5*x

Remember that x in this case is equal to the number of cinnamon doughnuts sold.

We also know that the number of chocolate doughnuts sold is 8 trays, from the information given, and we can plug this value into our equation and simplify:

6*8=5*x

48=5*x

Lastly, we divide both side by 5 to isolate the variable, x:

9.6=x



Therefore, the number of cinnamon doughnuts sold is 9.6 trays.