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.