Find the natural number which when added to its square gives a times the next natural number ?

unknown values: n

equation: n^2 + n = n+1

answer: 1

One number is 17 more than another. If the greater number is increased by 3, the result is 5 times the smaller. What are the numbers?

unknown values: x,y

equation: x = y + 17

equation: x + 3 = 5*y

answer: 22; 5

The difference of two numbers is 67. The larger number is three less than six times the smaller number. Find the numbers.

unknown values: x,y

equation: x - y = 67

equation: x = 6*y - 3

answer: {81; 14}

The difference of two numbers is 16. the greater number is 5 less than 4 times the smaller number. find the #s?

unknown values: x,y

equation: x - y = 16

equation: x = 4*y - 5

answer: {23; 7}

The sum of three numbers is 44. The difference between the largest and the smallest is 14, and the largest is equal to the sum of the two smaller numbers. Find the numbers.

unknown values: x,y,z

equation: x+y+z=44

equation: x - z = 14

equation: x = y + z

answer: {22; 14; 8}

find two consecutive integers such that the square of the sum of the two integers is 11 more than the smaller integer.

unknown values: n,n+1

equation: (n+n+1)^2 = 11 + n

answer: -2; -1

six more than the square of a number is seven times the number. find all such numbers

unknown values: n

equation: 6 + n^2 = 7*n

answer: 6 or 1

Eight more than the square of a number is six times the number?

unknown values: x

equation: x^2 + 8 = 6*x

answer: 4 or 2

the sum of the digits of a two-digit number is 6. if the digits are reversed, the new number is three times the original tens digit. find the original number

unknown values: x

equation: a+b=6

equation: 10*a+b=x

equation: 10*b+a = 3*a

answer: 51

the sum of the digits of a two-digit number is 9. if 45 is subtracted from the number, the digits of the number are reversed. find the number.

unknown values: x

equation: a+b=9

equation: 10*a+b=x

equation: x-45=10*b+a

answer: 72