the squares of 2 consecutive odd numbers differ by 88, what are the numbers?

the squares of 2 consecutive odd numbers differ by 88, what are the numbers?

unknown values: 2*k+1,2*k+3

equation: (2*k+1)^2 - (2*k+3)^2 = 88

answer: 21; 23 or -23; -21 | -23; -21

A certain two-digit number has a value that that is three times the sum of its digits. The units digit is one more than three times the tens digit. Find the number.

unknown values: n

equation: n = 10*a+b

equation: n = 3(a+b)

equation: b = 1 + 3*a

answer: 27

A two digit number has its digits sum equal to 11.If you reverse the digits of this number, the new two digit number is 27 more than the original two digit number. Find the number.

unknown values: n

equation: n = 10*a + b

equation: a + b = 11

equation: 10*b + a = 27 + 10*a + b

answer: 47

The sum of two numbers is 8 less than the first number. Their difference is 5 less than twice the second number. Find each of the numbers.

unknown values: x,y

equation: x+y = x - 8

equation: x - y = 2*y - 5

answer: -29; -8

A certain number is expressed by three digits whose sum is 10. The sum of the first and last digits is two-thirds (2/3) of the second digit, and if 198 is subtracted from the number, the digits will be reversed. What is the number?

unknown values: n

equation: n = 100*a + 10*b + c

equation: a + b + c = 10

equation: a + c = (2/3) * b

equation: n - 198 = 100*c + 10*b + a

answer: 361

Twice the difference of 7 times a number and 4 yields the same result as the same number increased by 6. What is the number?

unknown values: x

equation: 2(7*x - 4) = x + 6

answer: 14/13 | 1.077

The value of a two digit number is twice as large as the sum of its digits. If the digits were reversed, the resulting number would be 9 less than 5 times the original number. Find the original number.

unknown values: n

equation: n = 10*a + b

equation: n = 2(a+b)

equation: 10*b+a = 5*n - 9

answer: 18

The tens digit of a two-digit number is twice the units digit. If the digits are reversed, the new number is 36 less than the original number. Find the number.

unknown values: n

equation: n = 10*a + b

equation: a = 2*b

equation: 10*b + a = n - 36

answer: 84

The product of two consecutive even numbers is 12 more than the square of the smaller number. Form an equation and solve it to find the numbers

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

equation: 2*k * (2*k+2) = 12 + (2*k)^2

answer: 6; 8

Find three consecutive numbers such that the sum of one-fourth the first and one-fifth the second is five less than one-seventh the third.

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

equation: 1/4 * n + 1/5 * (n+1) = 1/7 * (n+2) - 5

answer: -16; -15; -14