Question ?Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 810calories. Three servings of ice cream and two servings of blueberry pie provides 1230 calories. Find the caloric content of each item.

We want to write and solve a system of equations to see how is the caloric content of two types of dessert.

We will see that a serving of ice cream has 214.5 calories, while a serving of blueberry pie has 297.75 calories.

To find the system of equations we need to see what information is given.

We know that:

If we define the variables:

From the given information we can write the equations:

1*c + 2*b = 810 cal

3*c + 2*b = 1230 cal.

Now we can try to solve this system.

To solve it, we can see that in both equations we have the term "2*b", so we can isolate it in both equations to get:

2*b = 810 cal - 1*c

2*b = 1239 cal - 3*c

Now we can write:

810 cal - 1*c = 2*b = 1239 cal - 3*c

810 cal - 1*c =  1239 cal - 3*c

Now we can solve this for c:

810 cal - 1*c =  1239 cal - 3*c

3*c - 1*c =  1239 cal - 810 cal

2*c = 429 cal

c = (429 cal)/2 = 214.5 cal

Now that we know the value of c, we can find the value of b.

2*b =  810 cal - 1*c = 810 cal - 214.5 cal = 595.5 cal

b = (595.5 cal)/2 = 297.75 cal.

Then we can see that a serving of ice cream has 214.5 calories, while a serving of blueberry pie has 297.75 calories.

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e) none of the above because the measure of angle cba is 101°

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.