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3 years ago

P, Q, and R are prime numbers such that 3P + 7Q + 15R = 102. What is Q?

Mathematics

1 answer:

77julia77 [94]3 years ago

8 0

Q is 3

Step-by-step explanation:

The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, ......

They have two factors only 1 and itself
All the them are odd numbers except 2 is an even number
1 is not a prime number because has only one factor

∵ P, Q and R are three prime numbers

∵ 3P + 7Q + 15R = 102

- Factorize 102 into prime numbers

∵ 102 ÷ 2 = 51

∵ 51 ÷ 3 = 17

∴ The prime factorization of 102 is 2 × 3 × 17

∵ 2 , 3 , 17 are prime numbers

- Put them in the equation above to find which one is P and

which is Q and which is R

∵ R has the greatest coefficient, then put R = the smallest prime 2

∵ P has the smallest coefficient, then put P = the greatest prime 17

∴ Q = The last prime 3

- Let us check the value of the left hand side

∵ Left hand side = 3(17) + 7(3) + 15(2) = 51 + 21 + 30 = 102

∵ Right hand side = 102

∴ The prime numbers are P = 17 , Q = 3 , R = 2

Q is 3

Learn more:

You can learn more about the prime numbers in brainly.com/question/4550858

#LearnwithBrainly

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Read 2 more answers

Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and

Natali [406]

Answers:

Total equation: x+y = 80
Legs equation: 2x+4y = 248
How many ducks? 36
How many cows? 44

====================================================

Further explanation:

x = number of ducks
y = number of cows

x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.

That equation can be solved to y = 80-x after subtracting x from both sides.

The legs equation is 2x+4y = 248 because...

2x = number of legs from all the ducks only
4y = number of legs from all the cows only
2x+4y = total number of legs from both types of animals combined

We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248

------------

Let's plug y = 80-x into the second equation and solve for x.

2x+4y = 248

2x+4( y ) = 248

2x+4( 80-x ) = 248

2x+320-4x = 248

-2x+320 = 248

-2x = 248-320

-2x = -72

x = -72/(-2)

x = 36

There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

y = 44

There are 44 cows.

------------

Check:

36 ducks + 44 cows = 80 animals total

36*2 + 44*4 = 72 + 176 = 248 legs total

The answers are confirmed.

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2 years ago