1. The largest of five consecutive integers is twice the smallest. Find the smallest integer.
2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers.
3. If each of three consecutive integers is divided by 3, the sum of the quotients is 84. Find the smallest integer.
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1. To find the smallest integer among five consecutive integers, let's represent the integers as x, x+1, x+2, x+3, and x+4 (where x is the smallest integer). The problem states that the largest integer is twice the smallest, so we can set up the equation: x+4 = 2x.
To solve this equation, we can subtract x from both sides: 4 = x. Therefore, the smallest integer is 4.
2. Let's represent the three consecutive integers as x, x+1, and x+2. The problem states that when their sum is divided by 9, the result is 7.
So, we can set up the equation: (x + x + 1 + x + 2) / 9 = 7.
Simplifying the equation, we have: (3x + 3) / 9 = 7.
Multiplying both sides by 9, we get: 3x + 3 = 63.
Subtracting 3 from both sides, we have: 3x = 60.
Dividing both sides by 3, we find: x = 20.
Therefore, the three consecutive integers are 20, 21, and 22.
3. Let's represent the smallest integer among the three consecutive integers as x. The problem states that when each of the three integers is divided by 3, the sum of the quotients is 84.
So, the equation we can set up is: (x / 3) + ((x+1) / 3) + ((x+2) / 3) = 84.
Combining like terms, we have: (3x + 3x + 1 + 3x + 2) / 3 = 84.
Simplifying further, we get: (9x + 3) / 3 = 84.
Multiplying both sides by 3, we have: 9x + 3 = 252.
Subtracting 3 from both sides, we get: 9x = 249.
Dividing both sides by 9, we find: x = 27.
Therefore, the smallest integer is 27.
x+4 = 2x
solve for x, the smallest.
(x + x+1 + x+2)/9 = 7
(x + x+1 + x+2)/3 = 84