Question

1.John’s age is 12 more than 2 times Sam’s age. The sum of their ages is 65. How old are John and Sam?

2.The difference between two numbers is 28. Find the two numbers if the larger number is 3 times the smaller number.

3.Mary and Jim collect baseball cards. Mary has five more than three times as many cards as Jim. The total number of cards they both have is 147. How many cards do they each have?

Answer 1

1. John is 47 1/3, Sam is 17 2/3.
2. 14 and 42
3. Jim has 35 1/2, Mary has 111 1/2

Explanation:

You want to know ages, numbers, and card counts given various relations between them:

1. John is 12 more than twice Sam's age; the sum is 65.
2. Larger is 3 times the smaller; the difference is 28.
3. Mary has 5 more than 3 times Jim; the sum is 147.

1. Ages

If s represents Sam's age, then (12 +2s) is John's age. The sum is ...

s + (12 +2s) = 65

3s = 53

s = 17 2/3

John's age is 65 -17 2/3 = 47 1/3

John is 47 1/3; Sam is 17 2/3.

2. Numbers

If x represents the smaller number, 3x is the larger number and the difference is ...

3x -x = 28

2x = 28

x = 14

The two numbers are 14 and 42.

3. Cards

If j represents the number of cards Jim has, then Mary has (5 +3j) and the total is ...

j +(5 +3j) = 147

4j = 142

j = 35.5

Mary has 147 -35.5 = 111.5

Mary has 111.5 baseball cards; Jim has 35.5.

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Additional comment

These problems are unusual in that ages and card counts are not integers. Checking the answers here, we find that they satisfy the problem statement, even though they don't make any real-world sense.

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