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# help with equations

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I need help with Algebra.

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?

Apr 30, 2023

#1
+32
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Let x be the largest integer.

First find the sum of the integers:

\(x+(x-1)+(x-2)+(x-3)+(x-4)+(x-5)+(x-6)\)

Simplify:

\(7x-21\)

Now, since the sum or 7x - 21 is 21 times the largest of the integers or x, we can solve for x:

\(7x-21=21x\)

\(-21=14x\)

\(-1.5=x\)

Now we know the largest of the integers is -1.5.

To find the smallest integer, all we need to do is subtract 6 from -1.5:

\(-1.5-6=-7.5\)

The smallest integer Pearl wrote down was -7.5.

Apr 30, 2023
#2
+135
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The smallest integer that Pearl wrote down is 15.

Step-by-step explanation:

7 consecutive integers. They are:

a

a+1

a+2

a+3

a+4

a+5

a+6

Sum of the integers:

a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 = 7a + 21

6 times the largest of the seven integers.

The largest is a + 6. So

7a + 21 = 6(a + 6)

7a + 21 = 6a + 36

7a - 6a = 36 - 21

a = 15

The smallest integer that Pearl wrote down is 15.

May 1, 2023