Each student in cooking class of 50 students is assigned to create a desert, an appetizer, or both. The total number of students creating an appetizer is 7 more than the number of students creating a desert. If the number of students that create two dishes is the same as the number of students that created one dish, how many students created a desert?

Hi Monique! With 50 students, 25 two-dish and 25 one-dish ... the offset of 7 more apps must be in the "one-dish" group ... "stair-step" 13a, 12d ... 15a, 10d ... 16a, 9d ... 9 desserts only plus 25 making desserts and apps ... 34 total dessert makers ... Regards :)

Let x be the number of students, who created only a dessert, y is the number of students who created only an appetizer. Then the number of students, who created two dishes, is 50-x-y (why?). We also have the following equations:

x+7+(50-x-y)=y+50-x-y or 57-y=50-x

x+y=50-x-y or x+y=25

So we got the following system:

y-x=7

y+x=25

Solve it for x and y, then calculate the number of students who created dessert. (Be careful here, it is not just x !)