Algebra 1: Section 2.11a
Solving Situational Problems
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Problem Set A covers the material in Section
1.1. The other Problem Sets cover additional
material added to the Algebra 1 program.
Directions for Set A: Write an expression that would represent each statement.
Problem Set A
1. Eighteen more that x
2. Five less than y
3. The sum of seven and g
4. Ten subtracted from h
5. The difference between seven and c
6. The quotient of eight and w
7. The product of g and nineteen
8. A third of the number y
9. The number d multiplied by twelve
10. Thirty-six divided by 5
11. The sum of m and n
12. The quotient of a and b
13. A fourth of g
14. The product of x and y
15. The difference between r and s
16. The sum of x and y multiplied by the
number f
17. Half of the product of m and n
18. The number g divided by the sum of
seven and k
19. The product of a and b increased by ten
20. Seven times the difference between d
and eleven
21. The number s divided by the product of
c and d
22. The difference of r and s, multiplied by t
23. The quotient of a and b increased by the
product of c and d
Directions for Set B: Write an equation that could be used to solve the problem.
Remember to define your variable. DO NOT solve the problem.
Problem Set B
1. Five more than a number is seventeen.
2. If seven is subtracted from six times a number the result is forty-three.
3. A number increased by ten is thirty-four.
4. One-half of a number decreased by five is negative eleven.
5. Ten times a number divided by three is twenty.
6. If three times a number is decreased by twelve the result is fifteen.
7. The product of two times a number and seven is forty-two.
8. The sum of five times and number and sixty-one is twenty-six.
9. Six more than one-fourth of a number is fifteen.
10. If the sum of a number and seven is divided by four, the result is nineteen more than the
original number.
Directions for Sets C to E: Solve each problem while showing sufficient work. Sufficient
work includes the following: 1) define your variable, 2) write an equation that will be used
to solve the problem, 3) show work while solving your equation, and 4) include the correct
label with your answer (if necessary).
Problem Set C
1. Nine more than a number is fifty-eight. What is the number?
2. A number decreased by eight is negative thirty-one. What is the number?
3. A basketball player scored thirty-seven points in a game. This was twelve points more than
he had scored in an earlier game. What was his score on the earlier game?
4. Three members of the School Committee missed the last meeting. Twelve members were
present at the meeting. How many members does the committee have?
5. If the temperature of the water in a beaker rises six degrees Celsius above what it is now, the
water will be at the boiling point (100 degrees Celsius). What is the temperature of the water
now?
6. Negative eight times a number is 376. What is the number?
7. One third of a number is –912. What is the number?
8. Daniel Erik paid $147 for six theater tickets. How much did each ticket cost?
9. The perimeter of a square lot is 156 m. How long is each side of the lot?
10. Twelve-year-old Lola is one fourth as old as her Uncle Hector. How old is Hector?
11. Six less than a number is twenty-two. Find the number.
12. If seventeen is subtracted from a number the result is thirty-five. What is the number?
13. Seven times a number equals negative seventy-seven, what is the number?
14. The length of a rectangle is four times its width. If the length is twenty inches, what is the
width?
15. Two-thirds of the students in the class are male. If eighteen of the students are male, how
many students are in the class? How many students are female?
16. If five-eights of a yard of a fabric costs four dollars, what is the price of one yard?
17. If three-quarters of a pound of coffee costs three dollars and ninety cents, what does one
pound of coffee cost?
18. Jerry is twice as old as Mary. If Jerry is twelve years old, how old is Mary?
19. Twelve times a number increased by nine is eighty-one. What is the number?
20. The perimeter of a rectangle is thirty-two inches. If the length is three times the width, what
is the area of the rectangle?
Problem Set D
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2.
3.
4.
5.
6.
7.
8.
The sum of two consecutive integers is 87. Find the numbers.
The sum of four consecutive integers is –106. Find the numbers.
The sum of four consecutive integers is –42. Find the numbers.
The sum of three consecutive odd integers is 81. Find the numbers.
The sum of three consecutive odd integers is 147. Find the numbers.
The sum of four consecutive even integers is –100. Find the numbers.
The sum of three consecutive even integers is 360. Find the numbers.
The sum of four consecutive even integers is the same as the smallest integer in the set. Find
the numbers.
9. The sum of four consecutive odd integers is 0. Find the numbers.
10. The greater of two consecutive even integers is six less than twice the smaller.
11. The smaller of two consecutive even integers is five more than one half of the greater.
12. The four Smith children were born at two-year intervals. The sum of their ages is 36.
13. The sum of three consecutive integers is 53 more than the least of the integers in the set.
Find the numbers.
14. A rectangle has a perimeter of 62 cm. The lengths in centimeters of its adjacent sides are
consecutive integers.
15. There are four consecutive integers. Three times the greatest is 6 more than the sum of the
other three.
Problem Set E
1.
2.
3.
4.
5.
The sum of 85 and twice a number is 237. Find the number.
Five times a number, decreased by 87, is –12. Find the number.
If you add 15 to the product of 4 and a number, you get 363. Find the number.
The perimeter of a rectangle is 326 and its length is 94. Find its width.
Eighteen-year-old Manolo is 4 years older than twice as old as his sister, Julia. How old is
Julia?
6. Find three consecutive integers whose sum is 81.
7. Find four consecutive odd integers whose sum is –112.
8. The lengths in meters of the sides of a triangle are consecutive even integers. The perimeter
is 210 m. How long is each side?
9. Two numbers differ by 3. Four times the lesser diminished by three times the greater is 7.
Find the numbers.
10. Find a number whose product with 7 is the same as its sum with 24.
11. The lengths of the sides of a triangle are consecutive even integers. Find the length of the
longest side if it is 14 units shorter than the perimeter.
12. Jim worked five less than twice as many hours as Jane did. How many hours did each work
if together they worked 97 hours?
13. The sum of the ages of Ruth and her mother is 77 years. The difference in their ages is 27
years. How old is each?
14. Find a number whose product with 9 is the same as its sum with 56
15. Three times a number, decreased by 8, is the same as twice the number, increased by 15.
Find the number.
16. The sum of two numbers is 15. Three times one of the numbers is 11 less than five times the
other. Find the numbers.
17. The greater of two consecutive integers is 15 more than twice the lesser. Find the integers.
18. Dina has 6 coins of equal mass. If she puts 5 of them in one pan of a beam balance and one
ball along with a mass of 100 g in the other pan, the pans balance each other. What is the
mass of each steel ball?
19. The lengths of the sides of a triangle are consecutive even integers. Find the length of the
longest side if it is 14 units shorter than the perimeter.
20. Mary has $6 more than Frank. Together Mary and Frank have $90 more than Joe, who has
half as much money as Frank. How much does Frank have?
21. Find four consecutive multiples of 4 such that twice the sum of the least and greatest exceeds
three times the least by 32.