Find three consecutive integers such that -5 times the sum of the first and the third is 24 greater than 4 times the opposite of the second.

Find three consecutive integers such that -5 times the sum of the first and the third is 24 greater than 4 times the opposite of the second.

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

equation: -5(n+(n+2)) = 24 + 4(-1 * (n+1))

answer: -5; -4; -3

Find this quantity: one half of the quantity multiplied by one third of the quantity equals 24.

unknown values: q

equation: (1/2)q * (1/3)q = 24

answer: 12 or -12

The tens digit of a two-digit number is 3 more than twice the units digit. If the digits are reversed, the new number is 54 less than the original number. Find the original number.

unknown values: n

equation: n = 10*a + b

equation: a = 3 + 2*b

equation: 10*b + a = n - 54

answer: 93

find the sum of odd numbers from 1 to 99, inclusive?

unknown values: s

equation: n=(99-1)/2+1

equation: s = (1+99)*n/2

answer: 2500

If the expression x^2 - kx - 12 is equal to zero when x=4, what is the value of k?

unknown values: k

equation: 4^2 - 4*k - 12 = 0

answer: 1

A 3- digit number in which one digit is the average of the other two digits is called an average number. 456 is an average number because 5 is the average of 4 and 6. How many three digit average numbers are there?

unknown values: n

equation: n = 9 * 5

answer: 45

what is 8% of 2,000.

unknown values: x

equation: x = 2000 * 0.08

answer: 160

what's 8% of 5.00?

unknown values: x

equation: x = 0.08 * 5

answer: 0.4

One fourth of one third is the same as one half of what fraction?

unknown values: x

equation: (1/4) * (1/3) = (1/2) * x

answer: 1/6

The denominator of a fraction exceeds the numerator by 4. When the fraction is reduced to lowest terms it is 2/3. What is the fraction?

unknown values: f

equation: d = n + 4

equation: n/d = 2/3

equation: f = n/d

answer: 8/12