Three cookies plus two donuts have 400 calories. Two cookies plus three donuts have 425 calories. Find how many calories are in a cookie and how many calories are in a donut?

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Answer 1 · 2018-02-23T10:00:49

Calories in a cookie $= 70$
Calories in a donut $= 95$

Let calories in cookies be $x$ and let calories in donuts be $y$ .

$(3x + 2y = 400) xx 3$

$(2x + 3y = 425) xx (-2)$

We multiply by $3$ and $-2$ because we want to make the $y$ values cancel each other so we can find $x$ (this can be done for $x$ also).

So we get :

$9x + 6y = 1200$
$-4x - 6y = -850$

Add the two equations so $6y$ will cancel

$5x = 350$

$x = 70$

Substitute $x$ with $70$

$3(70) +2y = 400$

$2y = 400-210$

$2y = 190$

$y = 95$

Answer 2 · 2018-02-23T10:11:14

We need to use simultaneous equations to solve this problem

Let the number of calories in a cookie be $x$ and the number of calories in a donut be $y$ .

$3x+2y=400" " " "(1)$

$2x+3y=425" " " " (2)$

From $(2)$

$2x=425-3y$

$x=(425-3y)/2" " " "(3)$

Sub $(3)$ into $(1)$

$3[(425-3y)/2]+2y=400$

$1275-9y+4y=800$

$-5y=-475$

$y=95" " " "(4)$

Sub $(4)$ into $(1)$

$3x+2(95)=400$

$x=70$

Therefore, each cookie has $70$ calories and each donut has $95$ calories.