Question

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $\frac{21}{4}$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

Answer 1

6

Explanation:

Let
`x` be the smallest integer and
`x+6` be the largest 7th integer:

`\displaystyle x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6)=(21)/(4)(x+6)\\\\7x+21=(21)/(4)x+(126)/(4)\\\\28x+84=21x+126\\\\7x+84=126\\\\7x=42\\\\x=6`

Therefore, the smallest integer that Pearl wrote down was 6.