Question

At Sunrise Donuts you can buy 6 donuts and 2 kolaches for $8.84. One kolache and 4 donuts would cost $5.36. What is the price of one donut at Sunrise Donuts?

Answer 1

Set up a system of equations like this, where "k" represents a kolache and "d" represents a donut:

$\left \{ {{6d +2k = 8.84} \atop {k+4d = 5.36}} \right.$

We're solving for d.  First, we can rearrange the second equation to have it equal k:

$k + 4d = 5.36$
$k = 5.36 - 4d$

Next, we can substitute this in for k in the first equation:

$6d + 2k = 8.84$
$6d + 2(5.36 - 4d) = 8.84$
$6d + 10.72 - 8d = 8.84$

Finally, we can get the value of d if we solve this equation:

$-2d + 10.72 = 8.84$
$-2d= -1.88$
$d = 0.94$

You can buy a donut at Sunrise Donuts for $0.94.