The sum of half a number and its reciprocal is the same as 51 divided by the number. Find the number.

unknown values: n

equation: n/2 + 1/n = 51/n

answer: 10 or -10

Three times the sum of twice a number and five is equal to five less than the number. What is the number?

unknown values: x

equation: 3(2*x+5) = x-5

answer: -4

Two numbers differ by 3. The sum of the larger and one fourth the smaller is 13. What are the numbers??

unknown values: x,y

equation: x-y=3

equation: x+y/4=13

answer: {11; 8}

The tens digit of a two-digit number is 1 less than five times the units digit. The square of the units digit is 5 less than the tens digit. Find the number.

unknown values: n

equation: n = 10*a + b

equation: a = 5*b - 1

equation: b^2 = a - 5

answer: 92

the tens digit of a two-digit number is 3 more than the units digit. the number is 8 more than six times the sum of the digits. What is the number?

unknown values: n

equation: n = 10*a + b

equation: a = 3 + b

equation: n = 8 + 6(a+b)

answer: 74

Find three consecutive even numbers such that the sum of the smallest and twice the second is 20 more than the third.

unknown values: 2*k,2*k+2,2*k+4

equation: 2*k + 2(2*k+2) = 20 + (2*k+4)

answer: 10; 12; 14

If three times the smaller of two consecutive even integers is added to the larger, the result is 4 more than three times the larger. Find the two numbers.

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

equation: 3*2*k + (2*k+2) = 4 + 3(2*k+2)

answer: 8; 10

I think of a number. I multiply the number by 5 and minus 60. I end up with the number i started with.What is my number?

unknown values: n

equation: 5*n - 60 = n

answer: 15

find a number whose product with 6 is the same as its sum with 45.

unknown values: n

equation: 6*n = 45 + n

answer: 9

Frida is thinking of number. She adds 15 to her number and finds that the result is 4 times her number. What is her number?

unknown values: n

equation: n + 15 = 4*n

answer: 5