Sum of three integers Practice Questions (Grade 7)

Question 1easy

Three numbers are in the ratio $1 : 2 : 3$ , and their sum is $84$ . What is the smallest number?

Let the numbers be $k$ , $2k$ , and $3k$ . Then $k + 2k + 3k = 84$ , so $6k = 84$ and $k = 14$ . The smallest is $k = 14$ .

Question 2easy

The sum of three numbers in the ratio $1 : 2 : 4$ is $63$ . What is the middle number?

Let the numbers be $k$ , $2k$ , and $4k$ . Then $k + 2k + 4k = 63$ , so $7k = 63$ and $k = 9$ . The middle is $2k = 2(9) = 18$ .

Question 3easy

Three numbers are in the ratio $3 : 5 : 8$ , and their sum is $96$ . What is the largest number?

Let the numbers be $3k$ , $5k$ , and $8k$ . Then $3k + 5k + 8k = 96$ , so $16k = 96$ and $k = 6$ . The largest is $8k = 8(6) = 48$ .

Question 4easy

The ages of three siblings are in the ratio $1 : 3 : 4$ , and the sum of their ages is $64$ years. What is the age of the middle sibling?

Let the ages be $k$ , $3k$ , and $4k$ . Then $k + 3k + 4k = 64$ , so $8k = 64$ and $k = 8$ . The middle age is $3k = 3(8) = 24$ .

Question 5easy

The sum of three numbers in the ratio $4 : 5 : 6$ is $90$ . What is the smallest number?

Let the numbers be $4k$ , $5k$ , and $6k$ . Then $4k + 5k + 6k = 90$ , so $15k = 90$ and $k = 6$ . The smallest is $4k = 4(6) = 24$ .

Question 6easy

The sum of three consecutive even integers is $42$ . What is the smallest integer?

Let the integers be $n$ , $n + 2$ , and $n + 4$ . Then $n + (n + 2) + (n + 4) = 42$ , so $3n + 6 = 42$ , $3n = 36$ , and $n = 12$ . The smallest is $12$ .

Question 7easy

The sum of three consecutive odd integers is $75$ . What is the largest integer?

Let the integers be $n$ , $n + 2$ , and $n + 4$ . Then $n + (n + 2) + (n + 4) = 75$ , so $3n + 6 = 75$ , $3n = 69$ , and $n = 23$ . The largest is $n + 4 = 27$ .

Question 8easy

The sum of three consecutive even integers is $84$ . What is the largest integer?

Let the integers be $n$ , $n + 2$ , and $n + 4$ . Then $n + (n + 2) + (n + 4) = 84$ , so $3n + 6 = 84$ , $3n = 78$ , and $n = 26$ . The largest is $n + 4 = 30$ .

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