Once the cake is removed from the oven, it has been exposed to the room temperature of 70°F. After 10 minutes, the cake's temperature decreased to 200°F, which is 150°F cooler than it initially was (350°F). As for the what is asked, 90°F is 260°F cooler than its original temperature (350°F).
This problem can be expressed in a ratio:
10mins:150°F = N:260°F
where N is how long it will take for cake to cool to 90°F
150°FxN=10x260
150N=2600
N=2600/150
N=17.33
N≈20 minutes
Thus, it takes approximately 20 minutes for the cake to cool to 90°F
