Clifford is making a cake for his sister's birthday. the recipe calls for 1.5 times as much flour as sugar.it also called for 1/2 as much butter as sugar all of the butter, flour, and sugar together total 7.5 cups write and solve an equation to determine how much of each ingredient clifford will need

flour:
butter:
Sugar:
total

First, we know that in total, all the butter, flour, and sugar will come out to 7.5 cups. Therefore, we can have 7.5 on one side of the equation we will be making, so now we just have to find what goes on the other side of the equation:

7.5 = ?

We know that butter is going to be used the last, as it uses half the amount of sugar, and to make the equation easier to read, we should start with the smaller values and end with bigger values. Since there is 1.5 times more flour than sugar, the order will be:

7.5 = butter + sugar + flour

Now, let us say that each ingredient is determined by the variable x, since x can represent the amount of sugar going into this cake, as all the other ingredients' measurements are being based on the sugar. Therefore, going in the butter, sugar then flour order, we can put how much less or more that ingredient needs to be than the sugar:

7.5 = 0.5x + x + 1.5x

Simplify:

7.5 = 3x

Divide 3 by both sides:

7.5(/3) = 3x(/3)

2.5 = x

So, because x represents sugar, we know that there will be 2.5 cups of sugar. Using the recipe, just multiply by 1.5 to find flour, and then by 0.5 to find butter, so the answer will be:

Flour: 3.25 cups

Butter: 1.75 cups

Sugar: 2.5 cups

And if you add those up, you get 7.5 cups.

Hope this helps :)