Calorie counting with pie

Question

Using the calorie count of one-eighth of a 9-in. pie, we find that the number of calories in a piece of pecan pie is 221 less than twice the number of calories in a piece of lemon meringue pie. If one eats a piece of each, a total of 865 calories is consumed. How many calories are there in each piece of pie? Please provide a check method.

Answer 1

Let's let x represent the number of calories in the pecan pie and y represent the number of calories in the lemon pie. Then since the sum of the calories for the two is 865 , we can write the following equation:

x + y = 865

Then since the number of calories in the pecan is 221 less than twice that of the lemon, we can write the following expression for the pecan :

2y - 221 = x

If we substitute 2y - 221 for x in our first equation, we can find the value of xy (or the calories in the lemon pie):

x + y = 865

2y - 221 + y = 865

Then combine liike terms and use inverse operations to solve for y:

3y - 221 = 865

3y -221 + 221 = 865 + 221

3y = 1086

3y/3 = 1086 /3

y= 362

So the number of calories in the lemon pie is 362. Since the sum of the two numbers is 865, the pecan pie (or x) will be 503 calories.

To verify, 2y- 221 for pecan:

2 * 362 - 221 = 503