Unit 2 Day 2
Date _______________
Writing and Solving Number Word Problems
CCS: A.CED.1
Warm-up:
a. Solve using ANY method:
A student is taking a test. He has 37 questions left. If the test has 78 questions, how many questions has he
finished?
b. Using t to represent the remaining test questions, write two different equations that you could use to
determine the answer to the problem above.
Word Problems: Use the following steps to translate a sentence into a mathematical equation and solve the equation.
1st: Choose a variable to represent the unknown quantity
2nd: Write a “Let statement” that identifies the variable and what it represents
Ex: Let n represent the number
Let t represent Tara’s age
3rd: Translate the sentence into an equation using the designated variable
4th: Follow the procedure to solve the equation
5th: Check your answer
6th: Write a sentence that answers the question
Number Word Problems
1.) The larger of two integers is four more than twice the smaller integer. The sum of the integers is 52. What
are the two integers?
SOLUTION: Let n represent the smaller integer
Let 4 + 2n represent the larger integer
Check:
n + 4 + 2n = 52 (translate the sentence into an equation)
Check from the words. Is the sum of the
two integers 52? 16 + 36 = 52 (yes!)
3n + 4 = 52 (combine like terms)
-4
3𝑛
3
=
-4 (Use the subtraction property of equality to solve for n)
48
3
(Use the division property of equality to solve for n)
n = 16
The smaller integer is 16. The larger integer is (2*16 +4)= 36.
Is the larger integer 4 more than twice
the smaller? 4 + (2*16)
4 + 32 = 36 (yes!)
Unit 2 Day 2
Date _______________
Writing and Solving Number Word Problems
CCS: A.CED.1
2.) A friend bought a bouquet of flowers. The bouquet had nine daisies and some roses. There were a total
of 15 flowers in the bouquet. How many roses were in the bouquet?
3.)
A student has been typing for 22 minutes and has typed a total of 1496 words. Write and solve an
equation to determine the average number of words she can type per minute.
4.) Ray’s birthday is 8 more than four times the number of days away from today than Jane’s
birthday. If Ray’s birthday is 24 days from today, how many days until Jane’s birthday?
5.) Jared weighs 15 pounds less than twice Kate’s weight. How much does Kate weigh if Jared
weighs 205 pounds?
Unit 2 Day 2
Date _______________
Writing and Solving Number Word Problems
CCS: A.CED.1
6.) A phone company charges a flat fee of $17 per month, which includes free local calling plus
$0.08 per minute for long distance calls. The Taylor’s phone bill for the month is $31.80. How
many minutes of long distance calling did they use during the month?
7.) A delivery company charges a flat rate of $3 for a large envelope plus an additional $0.25 per ounce for
every ounce over a pound the package weighs. The postage for the package is $5.50. How much does
the package weigh? (Hint: remember the first pound is included in the $3.)
8.) Vincent cut three pieces of rope to complete a science project. Two pieces are of equal length. The third
piece is one-quarter the length of each of the others. He cut the three pieces from a rope of 54 meters
long without any rope left over. Find the number of meters in each piece.
9.) Three numbers are in a ration 3:5:7. If the largest number is multiplied by 3, the result is 26 more than
the sum of the first and second numbers. Use an algebraic solution to find the numbers.