Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 800 calories. Three servings of ice cream and two servings of blueberry pie provides 1200 calories. Find the caloric content of each item.
1 i + 2 b = 800
3 i + 2 b = 1200
-------------------- subtract
-2 i = - 400
i = 200
200 + 2 b = 800
b = 300
ice cream calories ---- x
pie calories ---- y
x + 2y = 800 -----> x = 800-2y
3x + 2y = 1200
substitute:
3(800-2y) + 2y = 1200
2400 - 6y + 2y = 1200
-4y = -1200
y = 300
then x = 800-2(300) = 200
Well, well, well, it seems like Johnny's cafe is keeping their desserts a tasty secret! Let's solve this conundrum.
Let's assume that the caloric content of one serving of ice cream is "I" and the caloric content of one serving of blueberry pie is "B".
According to the first piece of information, we have the equation: I + 2B = 800.
And according to the second piece of information, we have this equation: 3I + 2B = 1200.
Now, let's solve this puzzle using my trusty mathematical skills!
First, let's multiply the first equation by 3, so it matches the second equation:
3(I + 2B) = 3(800) -> 3I + 6B = 2400.
Now we can compare the updated equation and the second equation:
3I + 6B = 2400
3I + 2B = 1200
Subtracting the second equation from the updated equation, we get:
3I + 6B - (3I + 2B) = 2400 - 1200
4B = 1200
B = 300.
Now that we have the caloric content of one serving of blueberry pie (B = 300), we can substitute it into the first equation to find the caloric content of one serving of ice cream:
I + 2(300) = 800
I + 600 = 800
I = 200.
Voilà! The caloric content of one serving of ice cream is 200, and the caloric content of one serving of blueberry pie is 300.
Now, go enjoy those desserts responsibly, my friend!
Let's assign variables to the caloric content of each item. Let's say one serving of ice cream has x calories, and one serving of blueberry pie has y calories.
From the given information, we know:
1 serving of ice cream + 2 servings of blueberry pie = 800 calories ...(Equation 1)
3 servings of ice cream + 2 servings of blueberry pie = 1200 calories ...(Equation 2)
To solve this system of equations, we will use a method called substitution.
From Equation 1, we can rewrite it as:
x + 2y = 800
Next, we can solve Equation 2 for x:
3x + 2y = 1200
Rearranging Equation 2 gives us:
3x = 1200 - 2y
x = (1200 - 2y) / 3
Now that we have the value of x in terms of y, we can substitute it into Equation 1:
(1200 - 2y) / 3 + 2y = 800
Simplifying this equation:
1200 - 2y + 6y = 2400
4y = 1200
y = 1200 / 4
y = 300
We have found that one serving of blueberry pie has 300 calories.
Next, we can substitute the value of y = 300 back into Equation 1:
x + 2(300) = 800
x + 600 = 800
x = 800 - 600
x = 200
We have found that one serving of ice cream has 200 calories.
Therefore, one serving of ice cream has 200 calories, and one serving of blueberry pie has 300 calories.
To find the caloric content of each item, let's assign variables to represent the number of calories in each serving.
Let:
- x be the number of calories in one serving of ice cream,
- y be the number of calories in one serving of blueberry pie.
From the information given, we can form two equations:
Equation 1: x + 2y = 800 (caloric content of one serving of ice cream and two servings of blueberry pie is 800 calories)
Equation 2: 3x + 2y = 1200 (caloric content of three servings of ice cream and two servings of blueberry pie is 1200 calories)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve using the method of elimination:
Multiply Equation 1 by 2 to make the coefficients of y equal:
2(x + 2y) = 2(800)
2x + 4y = 1600
Now, subtract Equation 2 from the new Equation 1 to eliminate y:
(2x + 4y) - (3x + 2y) = 1600 - 1200
2x + 4y - 3x - 2y = 400
Simplifying the equation further:
-x + 2y = 400
Now, let's solve for x:
Multiply Equation 1 by 3 to make the coefficients of x equal:
3(x + 2y) = 3(800)
3x + 6y = 2400
Now, subtract Equation 2 from the new Equation 1 to eliminate x:
(3x + 6y) - (3x + 2y) = 2400 - 1200
3x + 6y - 3x - 2y = 1200
Simplifying the equation further:
4y = 1200
Divide both sides by 4 to solve for y:
y = 1200 / 4
y = 300
Now that we have the value of y, we can substitute it back into either Equation 1 or Equation 2 to find x:
Using Equation 1:
x + 2(300) = 800
x + 600 = 800
x = 800 - 600
x = 200
Therefore, one serving of ice cream contains 200 calories, and one serving of blueberry pie contains 300 calories.