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# I don't understand

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The average of a sequence of n numbers is 10. If the numbers 20 and 30 are added to this sequence to form a sequence of n + 2 terms, the average of the sequence increases to 12. What is the value of n?

So I tried adding the two numbers 20 + 30 which increased the average by 2 which I can try to make an equation but I am having trouble continuing

Any ideas?

appreciate the help!! :))

Feb 1, 2022

#1
+1334
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For the original sequence: $${\text {sum}\over n } = 10$$

When you add the terms $$20$$ and $$30$$, we have the equation: $${{\text{sum} + 50}\over{n+2}} = 12$$

These two are a equations form a system, and you can solve for $$n$$ from here.

Good Luck!

Feb 1, 2022
#2
+39
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Thank you I got it from here!

I got

sum = 10n

soo

(10n+50)/(n+2)=12

cross multiplying we get

10n+50 = 12n+24

therefore we get n= 18

cosign  Feb 1, 2022
edited by cosign  Feb 1, 2022
#3
+1334
+2

$$18$$ is incorrect. Here is how you solve it:

$${\text {sum}\over n} = 10$$

$$\text {sum} = 10n$$

$${{10n+50}\over {n+2}} = 12$$

$${10n+50} = 12n+24$$

$$50 = 2n+24$$

$$26 = 2n$$

$$n=13$$

Thus, there are $$\color{brown}\boxed{13}$$ terms in the original sequence that make for a mean of $$10$$, and when the numbers $$20$$ and $$30$$ are added, the sum becomes $$180$$, making the mean $$12$$.

BuilderBoi  Feb 2, 2022