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Alja [10]
3 years ago
5

A student brings whole cherry and cheese danishes to his class for his birthday. The number of cherry danishes he brings is at l

east 3 more than $\frac{2}{3}$ the number of cheese danishes, but no more than twice the number of cheese danishes. Find the smallest possible value for the total number of danishes he brings.
Mathematics
2 answers:
Olegator [25]3 years ago
8 0

Answer:

8

yes its 8

8 is the correct answer

dont listen to the other guy

LenKa [72]3 years ago
3 0

Let the number cherry Danishes be x

Let the number cheese Danishes be y

 

Given,

The number of cherry Danishes the student brings is at least 3 more than 2/3 the number of cheese Danishes

x ≥ 3 + (2/3)y

 

Given,

The number of cherry Danishes the student brings is no more than twice the number of cheese Danishes.

x ≤ 2y

 

Merging, the two inequalities above,

3 + (2/3)y ≤ x ≤ 2y

3 + (2/3)y ≤ 2y

OR 2y ≥ 3 + (2/3)y

2y – (2/3)y ≥ 3

 

Multiply both sides by 3

(3 * 2)y – (3 * 2/3)y ≥ 3 * 3

6y – 2y ≥ 9

4y ≥ 9

y ≥ 9/4

 

Since x ≥ 3 + (2/3)y, and y ≥ 9/4

Then, x ≥ 3 + (2/3 * 9/4)

x ≥ 3 + (2/3 * 9/4)

x ≥ 3 + 3/2

x ≥ 9/2

 

Since y ≥ 9/4 and x ≥ 9/2

x + y ≥ 9/4 +9/2

x + y ≥ 27/4

x + y ≥ 6.75

 

 

x + y represents the total number of Danishes the student brings

x + y ≥ 6.75 means that the total number of Danishes the student brings is 6.75

 

<span>BUT since the total number of Danishes must be an integer, then that the total number of Danishes the student brings is 6.</span>

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