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Amaya's test scores in Algebra 1 are 78 and 91. She has one more test left and wants to earn a B for the course, which is from 80-89 inclusive. Write a compound inequality to represent the situation

Respuesta :

Let x be the score Amaya gets on the final test. She wants her average of all 3 tests to be between 80 and 89: 

80 ≤ (78 + 91 + x) / 3 ≤ 89 

Multiply everything by 3: 
240 ≤ 78 + 91 + x ≤ 267 
240 ≤ 169 + x ≤ 267 

Subtract 169 from everything: 
240 - 169 ≤ x ≤ 267 - 169 
71 ≤ x ≤ 98 

Answer: 
She needs to score between 71 and 98 to get a B for the course.
fichoh

The compound inequality expression expressing the required score to obtain a B grade is 80 ≤ (169 + t) ≤ 89

Test scores :

  • 78 and 91

Range of B - grade:

  • 80 - 89

Let the her score in the last test = t

Final average score will be :

  • (78 + 91 + t) / 3 = (169+t) / 3

To obtain a B grade :

  • 80 ≤ Final average score
  • Final average score ≤ 89

The compound inequality expression can be expressed thus :

  • 80 ≤ Final average score ≤ 89

Therefore, the compound inequality expression is 80 ≤ (169 + t) ≤ 89

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