my sisters keeper
101 Word Problems/Solutions
Problem #1: Antifreeze
A quart bottle contains a mixture that is 1/3 antifreeze, 2/3 water. A half gallon bottle contains a mixture that is 3/4 antifreeze, 1/4 water. The contents of the two bottles are poured into a gallon jug. What is the ratio (one integer to another, in the form a:b) of antifreeze to water in the jug?
Solution #1: Antifreeze
11:7
Problem #2: Consecutive Birthdays
A woman and her grandson have the same birthday. For six consecutive birthdays, she is an integral multiple of his age. How old is the grandmother at the sixth of these birthdays?
Solution #2: Consecutive Birthdays
66
Problem #3: Cube Numbers
Find all sets of four positive consecutive integers such that the sum of the cubes of the first three is the cube of the fourth.
Solution #3: Cube Numbers
3,4,5,6
Problem #4: Don't Spend It All At Once
If I start with $10 and spend all but $3, how much do I have left?
Solution #4: Don't Spend It All At Once
$3. If I spend all but $3, I must have $3 left.
Problem #5: Hands of a Clock
How many times do the two hands of a clock point in the same direction between 6:00 am and 6:00 pm of a single day?
Solution #5: Hands of a Clock
11. It is tempting to give the "obvious" answer 12, but the true answer is 11 as will be found by counting the individual occasions.
1. Between 6:30 am and 6:35 am.
2. Between 7:35 am and 7:40 am.
3. Between 8:40 am and 8:45 am.
4. Between 9:45 am and 9:50 am.
5. Between 10:50 am and 10:55 am.
6. At Noon.
7. Between 1:05 am and 1:10 am.
8. Between 2:10 am and 2:15 am.
9. Between 3:15 am and 3:20 am.
10. Between 4:20 am and 4:25 am.
11. Between 5:25 am and 5:30 am.
Problem #6: How Old Is My Daughter?
My daughter is twice as old as my son and half as old as I am. In twenty-two years my son will be half my age. How old is my daughter?
Solution #6: How Old Is My Daughter?
Let us assume my daughter is age x. We are told my daughter is twice
Problem #1: Antifreeze
A quart bottle contains a mixture that is 1/3 antifreeze, 2/3 water. A half gallon bottle contains a mixture that is 3/4 antifreeze, 1/4 water. The contents of the two bottles are poured into a gallon jug. What is the ratio (one integer to another, in the form a:b) of antifreeze to water in the jug?
Solution #1: Antifreeze
11:7
Problem #2: Consecutive Birthdays
A woman and her grandson have the same birthday. For six consecutive birthdays, she is an integral multiple of his age. How old is the grandmother at the sixth of these birthdays?
Solution #2: Consecutive Birthdays
66
Problem #3: Cube Numbers
Find all sets of four positive consecutive integers such that the sum of the cubes of the first three is the cube of the fourth.
Solution #3: Cube Numbers
3,4,5,6
Problem #4: Don't Spend It All At Once
If I start with $10 and spend all but $3, how much do I have left?
Solution #4: Don't Spend It All At Once
$3. If I spend all but $3, I must have $3 left.
Problem #5: Hands of a Clock
How many times do the two hands of a clock point in the same direction between 6:00 am and 6:00 pm of a single day?
Solution #5: Hands of a Clock
11. It is tempting to give the "obvious" answer 12, but the true answer is 11 as will be found by counting the individual occasions.
1. Between 6:30 am and 6:35 am.
2. Between 7:35 am and 7:40 am.
3. Between 8:40 am and 8:45 am.
4. Between 9:45 am and 9:50 am.
5. Between 10:50 am and 10:55 am.
6. At Noon.
7. Between 1:05 am and 1:10 am.
8. Between 2:10 am and 2:15 am.
9. Between 3:15 am and 3:20 am.
10. Between 4:20 am and 4:25 am.
11. Between 5:25 am and 5:30 am.
Problem #6: How Old Is My Daughter?
My daughter is twice as old as my son and half as old as I am. In twenty-two years my son will be half my age. How old is my daughter?
Solution #6: How Old Is My Daughter?
Let us assume my daughter is age x. We are told my daughter is twice