A. Four times one odd integer is 14 less than three times the next even integer. Find the integers.
B. The average of four consecutive odd integers is 16. Find the largest integer.
C. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers.
D. If each of three consecutive integers is divided by 3, the sum of the quotients is 84. Find the smallest integer.
A. Let x = odd, then x+1 = even
4x + 14 = 3(x+1)
Solve for x.
B. (x + x+1 + x+2 +x+3)/4 = 16
C. (x + x+1 + X+2)/9 = 7
I'll leave you to use a similar process to solve the last one.
the number B (?)
four consecutive odd integers
(X + X+2 + X+4 + X+6 ) /4 = 16
I'm not sure
D.
( x + x+1 + x+2 )/3=84
B. your equation is right, so X=13
Or, you can look at it as follows. If the average is 16, the odd numbers are evenly spaced above and below 16:
13,15,17,19
D.
again, your equation is correct. x=83
again, it's an average problem. The numbers are evenly spaced around 84:
83,84,85
A. Let's break down the problem step by step.
1. Let's assume the first odd integer as "x".
2. The next even integer will be "x + 1" because adding 1 to an odd integer gives the next even integer.
3. Four times the first odd integer is written as 4x.
4. Three times the next even integer is written as 3(x + 1).
Now, according to the problem, "Four times one odd integer is 14 less than three times the next even integer", so we can set up the equation:
4x = 3(x + 1) - 14
Simplifying the equation will give us:
4x = 3x + 3 - 14
4x = 3x - 11
Now, subtract 3x from both sides:
4x - 3x = -11
x = -11
So, the first odd integer is -11, and the next even integer is -11 + 1 = -10.
Hence, the two integers are -11 and -10.
B. Let's solve this problem step by step:
1. Let's assume the first odd integer as "x".
2. The next consecutive odd integer is "x + 2".
3. The third consecutive odd integer is "x + 4".
4. The fourth and largest integer is "x + 6".
According to the problem, the average of these four consecutive odd integers is 16. We can set up the equation:
(x + x + 2 + x + 4 + x + 6) / 4 = 16
Simplifying the equation will give us:
(4x + 12) / 4 = 16
Now, multiply both sides by 4 to get rid of the denominator:
4x + 12 = 64
Subtract 12 from both sides:
4x = 52
Divide both sides by 4:
x = 13
So, the largest integer is x + 6 = 13 + 6 = 19.
Hence, the largest integer is 19.
C. Let's solve this problem step by step:
1. Let's assume the middle consecutive integer as "x".
2. The previous consecutive integer will be "x - 1" because subtracting 1 from an integer gives the previous consecutive integer.
3. The next consecutive integer will be "x + 1".
According to the problem, when the sum of three consecutive integers is divided by 9, the result is 7. We can set up the equation:
(x - 1 + x + x + 1) / 9 = 7
Simplifying the equation will give us:
(3x) / 9 = 7
Now, multiply both sides by 9 to get rid of the denominator:
3x = 63
Divide both sides by 3:
x = 21
So, the three integers are x - 1 = 21 - 1 = 20, x = 21, and x + 1 = 21 + 1 = 22.
Hence, the three integers are 20, 21, and 22.
D. Let's solve this problem step by step:
1. Let's assume the smallest integer as "x".
2. The next consecutive integer will be "x + 1".
3. The third consecutive integer will be "x + 2".
According to the problem, if each of three consecutive integers is divided by 3, the sum of the quotients is 84.
We can set up the equation:
(x / 3) + ((x + 1) / 3) + ((x + 2) / 3) = 84
Simplifying the equation will give us:
(x + x + 1 + x + 2) / 3 = 84
3x + 3 = 252
Now, subtract 3 from both sides:
3x = 249
Divide both sides by 3:
x = 83
So, the smallest integer is 83.
Hence, the three integers are 83, 83 + 1 = 84, and 83 + 2 = 85.