Six more than a number is 3 times the number. What is the number?

unknown values: n

equation: n + 6 = 3*n

answer: 3

If a and b are the roots of x^2+8x-5=0, find the values of a^3+b^3 and a^3*b^3.

unknown values: m,n

equation: ab = -5

equation: a + b = -8

equation: m = a^3 + b ^3

equation: n = a^3 * b^3

answer: -632; -125

what is the sum of the first 100 even numbers

unknown values: s

equation: b = 2 + (100-1)*2

equation: s = (2+b)*100/2

answer: 10100

Find the sum of all the multiples of three between 1 and 100.

unknown values: s

equation: s = (99+3)n/2

equation: 3 + 3(n-1) = 99

answer: 1683

If a^2 + b^2 + c^2 = 99, and ab + bc + ac = 35, find the value of a + b + c.

unknown values: x

equation: a^2 + b^2 + c^2 = 99

equation: ab + bc + ac = 35

equation: x = a + b + c

answer: 13 or -13

If a-b=b-3=6, what is the value of a?

unknown values: a

equation: a-b = b-3

equation: b-3 = 6

answer: 15

a three-digit number satisfies the following conditions: the digits are consecutive whole numbers; the sum of the digits is greater than 10 and less than 20; and the tens digit is an odd number. What is the number?

unknown values: n

equation: n = 100*a + 10(a+1) + (a+2)

equation: a+(a+1)+(a+2) >10

equation: a+(a+1)+(a+2)

< 20 equation: is_odd(a+1) equation: is_digit(a, a+1, a+2) equation: a > 0 answer: 456 Given that a + b = 10 and a^2 - b^2 = 40, find the value of a - b. unknown values: a-b equation: a+b=10 equation: a^2-b^2=40 answer: 4 The quotient of a number and -7, decreased by 2, is 10. Find the number. unknown values: n equation: n/(-7) - 2 = 10 answer: -84 Nine less than the quotient of a number and 3 is 18. Find the number. unknown values: n equation: n/3 - 9 = 18 answer: 81