Tripling the greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer. What are the integers?

unknown values: n,n+2

equation: 3(n+2) = n-10

answer: -8; -6

The second of three numbers is 1 less than the first. The third number is 5 less than twice the second. If the third number exceeds the first number by 12, find the three numbers.

unknown values: x,y,z

equation: y = x - 1

equation: z = 2*y - 5

equation: z = x + 12

answer: 19; 18; 31

a two digit number is equal to four times the sum of its digits. If it is increased by 3, the resulting number is equal to three times the sum of its digits. Find the original number.

unknown values: n

equation: n = 10*a + b

equation: n = 4(a + b)

equation: n + 3 = 10*c + d

equation: n + 3 = 3(c + d)

equation: is_digit(a, b)

answer: 24

Twelve less than 2 times a number is equal to 15 minus 7 times the number.

unknown values: n

equation: 2*n - 12 = 15 - 7*n

answer: 3

The sum of the 32 terms in an arithmetic series is 5488 and the first term is 1. Find the last term in the series.

unknown values: x

equation: 1 + (32-1)*d = x

equation: (1+x)*32/2 = 5488

answer: 342

Find the reciprocal of (-1/2)(8/4)(12)

unknown values: x

equation: x * (-1/2)(8/4)(12) = 1

answer: -1/12 | -0.083

What is the sum of the consecutive integers from 15 to 55 (inclusive)?

unknown values: x

equation: x = (15 + 55)(55 - 15 + 1)/2

answer: 1435

If every number between 1 and 365 were added together, what would the total be?

unknown values: x

equation: x = (1+365)(365-1+1)/2

answer: 66795

Find the value of k so that the equation will have exactly one rational solution?2x^2+8x+k=0

unknown values: k

equation: 8^2 - 4*2*k = 0

answer: 8

the difference between two numbers is 2184. if the bigger number is 3 times the smaller number, find the sum of the two numbers.

unknown values: s

equation: s = m + n

equation: m - n = 2184

equation: m = 3*n

answer: 4368