Question

A brownie recipe for class 3 1/2 cups of sugar took one cup of chocolate chips. If one and three-quarter cups of sugar issues, but quantity of chocolate chips will be needed, according to the recipe?

Answer 1

The problem says "3 1/2 cups of sugar took one cup of chocolate chips"

The ratio is: 3 1/2 sugar for each cup of chocolate.

We want to find the quantity of chocolate chips for "one and three-quarter cups of sugar"

First, let's convert 3 1/2 into an improper fraction:

`3(1)/(2)=3+(1)/(2)=(3\cdot2)/(1\cdot2)+(1)/(2)=(6)/(2)+(1)/(2)=(7)/(2)`

Now, we want to find an expression for "one and three-quarter". We can write:

`1(3)/(4)=1+(3)/(4)=(4)/(4)+(3)/(4)=(7)/(4)`

And now, we can use cross multiplication. If 7/2 of sugar needs 1 cup of chocolate, how many of chocolate if 7/4 of sugar is used? If we call x to the quantity of chocolate needed, we can wirte:

`((7)/(2))/((7)/(4))=(1)/(x)`

Now take the reciprocal on both sides:

`((7)/(4))/((7)/(2))=x`

And solve:

`x=(7)/(4)\cdot(2)/(7)=(2)/(4)=(1)/(2)`

Thus, the answer is: According to the recipe, the quantity of chocolate needed is 1/2 cup.