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How many students created each item

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?

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4 Answers

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 :)

Number of students creating a dessert = d

Number of students creating an appetizer  = d + 7

Number of students creating two dishes = total number of students - total number creating single dish

= 50 - (d+d+7) = 50 -(2d+7)

According to the problem the above is equal to total number of students creating a single dish

50 - (2d+7) = 2d+7

solve for d:

4d+14 = 50

d = 36/4 = 9 students

 d= number making desert

d + 7 = number of students making appetizer

x = number of students making both dish

d+ d+7 - x= 50

2d +7 = x +50

 we have to solve this equation, only for an integer solution.

   x = 7 , only possible solution.

   d = 25 , total number of students who make desert and appetizer.

   25 includes students who make desert and desert and appetizer.

  rest of the 50 is divided between desert maker and appetizers makers.

  9 students make desert only , and 16 appetizers makers only.

  25 desert makers include 9 desert makers only, and 16 who make both desert and appetizer. 

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 !)