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3 years ago

9

Number Theory- Find all sets of the two consecutive positive integers with a sum that is at least 8 and less less than or equal

to 24.

1 answer:

leva [86]3 years ago

8 0

Answer:

Step-by-step explanation:

Let the smaller number = x

Let the larger number = x + 1

(4,5)

(5,6)

(6,7)

(7,8)

(8,9)

(9,10)

(10,11)

(11,12)

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There is a competition in the cinema to win free tickets. You must guess the ages of the four employees. Here are the clues: - W

jenyasd209 [6]

Answer:

Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old.

Step-by-step explanation:

Let $k$ be Kirk's age.

Let $b$ be Brian's age.

Let $m$ be Matt's age.

Let $m_{1}$ be the boss/manager's age.

From the information given, we can set up 4 equations:

$k+b+m+m_{1}=106$

$k=2(m_{1}-10)$

$b=2m_{1}-12$

$m=\frac{1}{2}m_{1}+6$

Rewrite the first equation, substituting $k$ , $b$ , and $m$ in terms of $m_{1}$ to get:

$2(m_{1}-10)+(2m_{1}-12)+(\frac{1}{2}m_{1}+6)+m_{1}=106$

Open up the parentheses using the distributive property (which is $a(b-c)=ab-ac$ ) and combine like terms to get:

$5.5m_{1}-26=106$

Add 26 to both sides to reach:

$5.5m_{1}=132$

Thus, $m_{1}=24$ . Substitute $24$ for $m_{1}$ in the second, third, and fourth original equations to find that $k=28$ , $b=36$ , and $m=18$ . Therefore, Kirk is <u>28</u> years old, Brian is <u>36</u> years old, Matt is <u>18</u> years old, and the manager is <u>24</u> years old. To check, you can add up all of the ages to get 106.

Hope this helps :)

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