# 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?

Feb 23, 2018

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

#### Explanation:

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

$\left(3 x + 2 y = 400\right) \times 3$

$\left(2 x + 3 y = 425\right) \times \left(- 2\right)$

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 :

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

Add the two equations so $6 y$ will cancel

$5 x = 350$

$x = 70$

Substitute $x$ with $70$

$3 \left(70\right) + 2 y = 400$

$2 y = 400 - 210$

$2 y = 190$

$y = 95$

Feb 23, 2018

We need to use simultaneous equations to solve this problem

#### Explanation:

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

$3 x + 2 y = 400 \text{ " " } \left(1\right)$

$2 x + 3 y = 425 \text{ " " } \left(2\right)$

From $\left(2\right)$

$2 x = 425 - 3 y$

$x = \frac{425 - 3 y}{2} \text{ " " } \left(3\right)$

Sub $\left(3\right)$ into $\left(1\right)$

$3 \left[\frac{425 - 3 y}{2}\right] + 2 y = 400$

$1275 - 9 y + 4 y = 800$

$- 5 y = - 475$

$y = 95 \text{ " " } \left(4\right)$

Sub $\left(4\right)$ into $\left(1\right)$

$3 x + 2 \left(95\right) = 400$

$x = 70$

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