Question

A brownie recipe asks for two and two thirds times as much sugar as chocolate chips. If four and one third cups of sugar is used, what quantity of chocolatechips would then be needed, according to the recipe?0308X5?

Answer 1

Let's call C to the cups of chocolate chips and S to the cups of sugar. We are told that the cups of sugar are 2 2/3 times the cups of chocolate, then we can formulate the following equation:

`S=2(2)/(3)C`

In the case 4 1/3 of sugar is added, we can replace 4 1/3 for S to get:

`4(1)/(3)=2(2)/(3)C`

By dividing both sides by 2 2/3 we get:

`\begin{gathered} 4(1)/(3)/2(2)/(3)=2(2)/(3)C/2(2)/(3) \\ 4(1)/(3)/2(2)/(3)=C \end{gathered}`

We can rewrite the mixed fractions to get:

`\begin{gathered} (4*3+1)/(3)/(2*3+2)/(3)=C \\ (12+1)/(3)/(6+2)/(3)=C \\ (13)/(3)/(8)/(3)=C \end{gathered}`

By changing the division symbol to a multiplication symbol and flipping the 8/3, we get:

`\begin{gathered} (13)/(3)*(3)/(8)=C \\ (13)/(8)=C \\ (8+5)/(8)=C \\ (8)/(8)+(5)/(8)=C \\ 1+(5)/(8)=C \\ 1(5)/(8)=C \\ C=1(5)/(8) \end{gathered}`

Then, 1 5/8 cups of chocolate chips are needed