find the second of the three consecutive positive even integers such that the product of the first and second is 64 less than the square of the third

find the second of the three consecutive positive even integers such that the product of the first and second is 64 less than the square of the third

unknown values: n

equation: (n-2)n = (n+2)^2 - 64

answer: 10

find 3 consecutive integers such that the product of all 3, decreased by the cube of the first, is 33

unknown values: n,n+1,n+2

equation: n(n+1)(n+2) - n^3 = 33

answer: 3; 4; 5

The sum of 3 numbers is 137. The second number is 4 more than 2 times the first number. The third is 5 less than three times the first number. Find the 3 numbers

unknown values: x,y,z

equation: x+y+z=137

equation: y = 4 + 2*x

equation: z = 3*x - 5

answer: 23; 50; 64

Twice the sum of a number and 8 is 40. Find the number

unknown values: x

equation: 2*(x+8)=40

answer: 12

The sum of three integers is 61. The sum of the first and second exceeds the third by 71. The third integer is 36 less than the first. Find the three integers.

unknown values: x,y,z

equation: x+y+z=61

equation: x+y=z+71

equation: z=x-36

answer: 31; 35; -5

The product of two positive integers is 64. Determine the two integers if one number is 4 times the other.

unknown values: x,y

equation: xy = 64

equation: x = 4*y

equation: x >0

equation: y >0

answer: {16; 4}

what is the smallest of three positive consecutive odd integers if the product of the second and third integers is 63?

unknown values: n

equation: (n+2)(n+4) = 63

answer: 5

Eight times the sum of three consecutive even integers is 108 more than 21 times the smallest of three integers

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

equation: 8*((2*k-2)+2*k+(2*k+2))=21*(2*k-2)+108

answer: 20; 22; 24

One number is twice another number. When the larger is diminished by 10, the result is 2 greater than the smaller. Find the numbers.

unknown values: x, y

equation: x = 2*y

equation: x - 10 = y + 2

answer: 24; 12

There are three consecutive odd integers, such that three times the first, minus two times the second, plus 13, equals negative three times the sum of the first and the third. What is the first integer?

unknown values: 2*k-1

equation: 3(2*k-1)-2(2*k+1)+13=-3((2*k-1)+(2*k+3))

answer: -3