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# Help needed quick

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Plz help from smart guys I dont know

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

Aug 2, 2023

#1
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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to \$21\$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

Let the smallest integer be represented by x.

Since the integers are consecutive, each following

integer is one larger than the integer before it.

(x)  +  (x + 1)  +  (x + 2)  +  (x + 3)  +  (x + 4)  +  (x + 5)  +  (x + 6)  =  (21) • (x + 6)

7x + 21  =  21x + 126

Subtract 7x from both sides

21  =  14x + 126

Subtract 126 from both sides

–105  =  14x

Divide both sides by 14

x  =  –7.5

(–7.5) + (–6.5) + (–5.5) + (–4.5) + (–3.5) + (–2.5) + (–1.5)  =  (21) • (–1.5)

–31.5  =  –31.5

.

Aug 2, 2023

#1
+945
+1

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

Let the smallest integer be represented by x.

Since the integers are consecutive, each following

integer is one larger than the integer before it.

(x)  +  (x + 1)  +  (x + 2)  +  (x + 3)  +  (x + 4)  +  (x + 5)  +  (x + 6)  =  (21) • (x + 6)

7x + 21  =  21x + 126

Subtract 7x from both sides

21  =  14x + 126

Subtract 126 from both sides

–105  =  14x

Divide both sides by 14

x  =  –7.5