“FUN” PROBLEM #5

1. The sum of two numbers is 19. Five times the lesser number is four more than twice the greater.

What are the numbers?

2. The difference between two numbers is 12. Six times the lesser number is 8 more than four times

the greater. Find the numbers.

3. The Governor’s mansion is three times as old as the State House. Fifteen years ago the mansion

was six times as old as the State House was. How old are these buildings?

4. Mr. Rojas is four times as old as his son Alex. Eighteen years from now he will be twice as old as

Alex will be. How old are Mr. Rojas and Alex?

5. Mrs. Sims always claims to be 5 years younger than she really is. What is her real age if 2 1/2 times

her age is 3 times her claimed age?

6. To impress visitors to his village, an elderly farmer always claims to be 20 years older than he really is.

The sum of his real age and his claimed age is 2 1/2 times what his real age was 8 years ago.

How old is he?

7. The perimeter of a rectangle is 40 centimeters. Four times the length is 3 centimeters more than

seven times the width. Find the dimensions of the rectangle.

8. The perimeter of an isosceles triangle is 36 meters. Five times the length of the base is 2 meters

less than three times the length of each of the congruent sides. How long is each side of the triangle?

9. A 156-gram orange has 11 more calories than a pear weighing 79 grams, and 44 fewer calories

than a banana weighing 100 grams. If five such oranges have 10 fewer calories than two bananas and

two pears. How many calories does one of these oranges have?

10. A cup of coffee contains 20 more milligrams of caffeine than a cup of tea and 85 more milligrams of

caffeine than the average cola drink. If one cup of tea and four cola drinks contain the same amount of

caffeine as one cup of coffee, how many milligrams of caffeine are there in one cup of coffee?