一个美术生
What is the number x in 2+x/7 = 20/7?
unknown values: x
equation: 2+x/7 = 20/7
answer: 6
The sum of two consecutive integers is -313. Find the larger integer?
unknown values: y
equation: x + 1 = y
equation: x + y = -313
answer: -156
The first and second terms of a geometric sequence have a sum of 15, while the second and third terms have a sum of 60. Use an algebraic method to find the first three terms.
unknown values: a,ar,a*r^2
equation: a + ar = 15
equation: ar + a*r^2 = 60
answer: 3; 12; 48
if the sum of lcm and gcd of 2 consecutive numbers is 157, what is the sum of these numbers?
unknown values: s
equation: s = n + (n+1)
equation: 1 + n(n+1) = 157
answer: 25 | 25 or -25
If x + y = 4, and x + z = 9, what is the value of ( y - z)?
unknown values: y-z
equation: x + y = 4
equation: x + z = 9
answer: -5
How many positive integers less than 1,000 do not have 7 as any digit?
unknown values: n
equation: n = 9 * 9 * 9 - 1
In an arithmetic progression, the 8th term is three times the 3rd term and the 10th term is 19. Find the common difference and the sum of the terms from the 3rd to the 9th term inclusive.
unknown values: d,s
equation: a + (8-1)*d = 3(a + (3-1)*d)
equation: a + (10 - 1)*d = 19
equation: s = ((a + (3-1)*d) + (a + (9-1)*d))*(9-3+1)/2
answer: 2; 77
The sum of one half of a number, one third of that number, and one fourth of the same number is one tenth. What is the number?
unknown values: x
equation: 1/2*x + 1/3*x + 1/4*x = 1/10
answer: 6/65 | 0.0923
If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction.
unknown values: r
equation: (n+3)/d = 3/4
equation: n/(d-7)=1
equation: r = n/d
answer: 9/16
Which two consecutive whole numbers is square root of 29 between?
unknown values: k,k+1
equation: k^2
< 29 equation: (k+1)^2 > 29 answer: 5; 6