The sum of two consecutive prime numbers is 52. Their difference is 6. Find the prime numbers. Please Help!!!!
2006-07-13 16:12:59 · 11 answers · asked by Christine 2 in Education & Reference ➔ Homework Help
Solve with variables: let n = the first number, n-6 be the second since their difference is six.
n+ (n-6) = 52
2n - 6 = 52
2n = 58
n = 29
So your primes are 29 and 29-6 or 23.
2006-07-13 16:17:48 · answer #1 · answered by purplekitten 5 · 3⤊ 3⤋
Actually, you don't need to know that they are prime. The fact that they total 52 and are 6 apart is enough.
If the smaller number is x, then the larger number is x+6, so the total of the two numbers is 2x+6.
The total is also 52, so we know that 2x+6 = 52.
Therefore, 2x must be 46.
And x (the smaller number) must be 23.
The larger number is 6 more than 23, so it is 29.
It turns out that the two numbers (23 and 29) are prime, so the solution fits the problem.
2006-07-13 16:19:15 · answer #2 · answered by actuator 5 · 0⤊ 0⤋
23+29=52
2006-07-13 16:16:33 · answer #3 · answered by Starry 4 · 0⤊ 0⤋
29 and 23
2006-07-14 05:01:09 · answer #4 · answered by fzaa3's lover 4 · 0⤊ 0⤋
Let the first number to be x and the second number to be y.
x+y=52
x-y=6
2x=58
x=29
29+y=52
y=23
so, the two consecutive prime number is 29 and 23
2006-07-13 23:32:19 · answer #5 · answered by R@inY 3 · 0⤊ 0⤋
23 & 29
2006-07-13 16:16:47 · answer #6 · answered by Anonymous · 0⤊ 0⤋
x + y = 52
y = 52 - x
x - y = 6
x - (52 - x) = 6
x - 52 + x = 6
2x = 58
x = 29
y = 52 - x
y = 52 - 29
y = 23
2006-07-13 17:18:14 · answer #7 · answered by creative 3 · 0⤊ 0⤋
23 and 29. :)
2006-07-13 16:17:23 · answer #8 · answered by Chreap 5 · 0⤊ 0⤋
x+y=52
x-y=6
adding the left sides we get 2x
adding the right sides we get 58
so 2x=58
x = 29
then by substitution, y = 23
2006-07-13 16:16:57 · answer #9 · answered by smm9909 1 · 0⤊ 0⤋
x + y = 52
x - y = 6
Add the two equations
2x + y - y = 58
2x = 58
x = 29
y = 23
both prime!
2006-07-13 17:18:49 · answer #10 · answered by Anonymous · 0⤊ 0⤋