Three integers in a given ratio Practice Questions (Grade 7)

Warm-upeasy

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 $2k = 2(9) = 18$ .

Mid-gameeasy

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 $8k = 8(6) = 48$ .

Mid-gameeasy

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 $3k = 3(8) = 24$ .

Mid-gameeasy

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 $4k = 4(6) = 24$ .

Mid-gameeasy

Three integers are in the ratio $2 : 5 : 7$ , and their sum is $98$ . What is the middle integer?

Let the integers be $2k$ , $5k$ , and $7k$ . Then $2k + 5k + 7k = 98$ , so $14k = 98$ and $k = 7$ . The middle integer is $5k = 5(7) = 35$ .

Mid-gameeasy

The sum of three numbers in the ratio $5 : 4 : 3$ is $96$ . What is the smallest number?

Let the numbers be $5k$ , $4k$ , and $3k$ . Then $5k + 4k + 3k = 96$ , so $12k = 96$ and $k = 8$ . The smallest is $3k = 3(8) = 24$ .

Mid-gameeasy

A set of three numbers is in the ratio $2 : 3 : 7$ . If the numbers add to $120$ , what is the largest number?

Let the numbers be $2k$ , $3k$ , and $7k$ . Then $2k + 3k + 7k = 120$ , so $12k = 120$ and $k = 10$ . The largest is $7k = 7(10) = 70$ .

Buzzer beatereasy

The ages of three cousins are in the ratio $2 : 3 : 5$ , and the sum of their ages is $80$ years. What is the age of the middle cousin?

Let the ages be $2k$ , $3k$ , and $5k$ . Then $2k + 3k + 5k = 80$ , so $10k = 80$ and $k = 8$ . The middle age is $3k = 3(8) = 24$ .

Three integers in a given ratio (ACT). Game on.