Question

Three lemon cremes plus two fudge cookies have 400 calories. Two lemon cremes plus three fudge cookies have 425 calories. How many calories are in each kind of cookie?

Answer 1

In this problem, we can use the method of elimination to find the number of calories in a lemon creme and a fudge cookie. By setting up two equations and eliminating one variable, we can solve for the number of calories in each type of cookie. In this case, a lemon creme has 70 calories and a fudge cookie has 95 calories.

Step-by-step explanation:

Let's represent the number of calories in a lemon creme as x and the number of calories in a fudge cookie as y. From the given information, we can set up two equations:

3x + 2y = 400

2x + 3y = 425

Using the method of elimination, we can multiply the first equation by 2 and the second equation by 3 to eliminate x:

6x + 4y = 800

6x + 9y = 1275

Subtracting the first equation from the second equation, we get:

5y = 475

Dividing both sides by 5, we find that y = 95. Substituting this value into the first equation, we can solve for x:

3x + 2(95) = 400

3x + 190 = 400

3x = 210

x = 70

Therefore, a lemon creme has 70 calories and a fudge cookie has 95 calories.

Answer 2

Answer: lemon cremes contain 70 calories. fudge cookies contains 95 calories

Step-by-step explanation:

Let x represent the amount of calories in lemon cremes.

Let y represent the amount of calories in fudge cookies.

Three lemon cremes plus two fudge cookies have 400 calories. This means that

3x + 2y = 400 - - - - - -- - - - -1

Two lemon cremes plus three fudge cookies have 425 calories. This means that

2x + 3y = 425- - - - -- - - - - - 2

Multiplying equation 1 by 2 and equation 2 by 3, it becomes

6x + 4y = 800

6x +9y = 1275

Subtracting,

-5y = - 475

y = - 475/- 5

y = 95

Substituting y = 95 into equation 1, it becomes

3x + 2×95 = 400

3x = 400 - 190 = 210

x = 210/3 = 70

x = 70