One number is seven more than twice another. If their sum is decreased by nine, the result is thirteen. Find the numbers.

unknown values: x,y

equation: x = 7 + 2*y

equation: (x+y) - 9 = 13

answer: {17; 5}

A certain number has four digits, the sum of which is 10. If you exchange the first and the last digits, the new number will be 2997 larger. If you exchange the middle two digits of the original number, the new number will be 90 larger. This last enlarged number plus the original number equals 2558. What is the original number?

unknown values: n

equation: n = 1000*a + 100*b + 10*c + d

equation: a + b + c + d = 10

equation: 1000*d + 100*b + 10*c + a = 2997 + n

equation: 1000*a + 100*c + 10*b + d = 90 + n

equation: (90 + n) + n = 2558

answer: 1234

the sum of my two digits is 13. I am not divisible by 2. List all the possible numbers I could be.

unknown values: n

equation: n = 10*a + b

equation: a + b = 13

equation: is_odd(n)

equation: is_digit(a)

equation: is_digit(b)

answer: 49 or 67 or 85

what is the sum of the roots of the equation?: 2x^2+6x-7=0?

unknown values: s

equation: s = -1 * 6 / 2

answer: -3

What is the sum of the arithmetic sequence 152, 138, 124, ��, if there are 24 terms?

unknown values: s

equation: d = 138 - 152

equation: b = 152 + (24-1)d

equation: s = (152 + b)*24/2

answer: -216

Find two consecutive odd numbers such that the sum of one-fifth of the smaller and four-sevenths of the larger is equal to fifty-nine.

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

equation: 1/5 * (2*n-1) + 4/7 * (2*n+1) = 59

answer: 75; 77

Find the number of positive integral divisors of 23625.

unknown values: n

equation: n = (3+1)(3+1)(1+1)

answer: 32

the first three terms of an arithmetic series have a sum of 24 and a product of 312. what is the fourth term?

unknown values: x,a,d

equation: a + (a+d) + (a+2*d) = 24

equation: a(a+d)(a+2*d) = 312

equation: x = a + 3*d

answer: 18 or -2

The product of two consecutive integers is 2 less than the square of the smaller integer. Find the larger of the two integers.

unknown values: n+1

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

answer: -1

The difference of the sum and product of two integers is equal to the sum of their product and difference, and the product of their difference and sum is equal to the difference of their product and sum. What is are the possible values of the product of their sum and difference?

unknown values: m

equation: (x+y) - xy = xy + (x-y)

equation: (x-y) * (x+y) = xy - (x+y)

equation: m = (x+y) * (x-y)

answer: 0