The product of the two-digit number and its tens digit is 54. Find the number if the sum of the digits when added to the number gives a result of 36?

unknown values: 10*x+y

equation: (10*x+y)*x=54

equation: 10*x+y+x+y=36

answer: 27

The sum of a number and twice its reciprocal is 3. Find the numbers

unknown values: x

equation: x+2*(1/x)=3

answer: 1 or 2

Find two consecutive odd integers such that the sum of the smaller and twice the larger is 79

unknown values: 2*k-1,2*k+1

equation: (2*k-1)+2*(2*k+1)=79

answer: 25; 27

One third of a number is -92. Find the number

unknown values: x

equation: x/3=-92

answer: -276

The sum of two consecutive even integers is ten less than twice their product. Find their integers using factoring.

unknown values: 2*x,2*x+2

equation: (2*x+2*x+2)+10=2*2*x*(2*x+2)

answer: 2;4

Find three positive integers whose sum is 30 and whose product is 840?

unknown values: x,y,z

equation: x+y+z=30

equation: x*y*z=840

answer: {6;10;14}

The smaller of two consecutive even integers is 2 more than twice the larger. Find the numbers.

unknown values: 2*x,2*x+2

equation: 2*x=2+2*(2*x+2)

answer: -6;-4

a number, twice that number, and one-third of that number are added. The result is 20. What is the original number?

unknown values: x

equation: x + 2*x + (1/3)x = 20

answer: 6

Find four consecutive even integers such that four times the fourth decreased by one half the second is 9.

unknown values: 2*x,2*x+2,2*x+4,2*x+6

equation: 4*(2*x+6)-(2*x+2)/2=9

answer: -4;-2;0;2

a three-digit number, which is divisible by 10, has a hundreds digit that is one less than its tens digit. the number also is 52 times the sum of its digits. find the number

unknown values: 100*x+10*y

equation: x=y-1

equation: 100*x+10*y=52*(x+y)

answer: 780