Problem Solving and the Common Core

Appendix

Problem Sets

Translating words into algebraic expressions

1. Take a number and add 8.
2. Take a number and reduce it by 5.
3. Take a number and multiply by 3.
4. Take a number and multiply it by one half.

1. Add 8 to twice a number.
2. 5 fewer than half of a number.
3. 3 times one less than a number.
4. One half of three times a number.

Translating words into one and two-step equations

1. 8 more than a number is 15.
2. 5 fewer than a number is 20.
3. 3 times a number is 9.
4. One half of a number is 100.

1. 8 more than twice a number is 28.
2. 5 fewer than half a number is 20.
3. Half of 3 fewer than a number is 10.
4. 3 times one less than a number is 24.
5. One half of three times a number is 15.

Solving Multi-Step Equations with Real World Context

Monica made some cookies on Monday using a recipe her mother had given her. On Tuesday, she doubled the recipe and on Wednesday she tripled the recipe. After three days, Monica had 60 cookies, how many cookies did the original recipe make?

Let x be the number of cookies in the original recipe,

x + 2x + 3x = 60

Monica had some cookies, she gave half to her sister and then ate five and still had four left over. How many cookies did she have originally?

Let x be the number of cookies Monica had originally,

x – 1/2x – 5 = 4

Monica made some cookies, her sister made half as many. They combined their cookies and ate ten of them, if they had 8 left over, how many did Monica make?

Let x be the number of cookies Monica made,

x + 1/2x -10 = 8

Monica had some cookies; her sister had three times as many. If they combined their cookies and then gave half of the total to a neighbor, how many cookies did Monica make if they gave their neighbor ten cookies?

Let x be the number of cookies Monica made,

(x + 3x) / 2 = 10

Monica had some cookies. She gave seven to her sister. Monica then gave half of the remaining cookies to a neighbor, and she still had five cookies. How many cookies did she have originally?

Let x be the number of cookies Monica had,

(x-7) / 2 = 5

Monica made some cookies and then bought a package of 12 cookies. Monica’s sister made double the amount that Monica made herself. Together they now have 36 cookies, how many did Monica have to begin with?

Let x be the number of cookies Monica made originally,

x + 12+ 2x = 36

Monica made some pies to sell at the bake sale. The school cafeteria contributed four pies to the sale. Each pie was then cut into five pieces and sold. There were a total of 60 pieces to sell. How many pies did Monica make?

Let x be the number of pies Monica made for the bake sale,

5 (x + 4) = 60

Monica needed to make 100 cookies for her school bake sale. She saved 1/5^th of each batch for her own family. If she had to make five batches to have enough for the bake sale, how many cookies were in each batch?

Let x be the number of cookies in each batch,

100 = 5 (x – 1/5x)

Monica’s cookie recipe called for chocolate chips. She bought a total of 36 ounces of chocolate chips. In her first batch of cookies she used a set number of chocolate chips and then to experiment she used twice as many chocolate chips as she did in the first batch for her second batch. To continue the experiment she used half as many chocolate chips in her first batch in her third batch. If she used all 36 ounces in the three batches, how many chocolate chips were in the first batch?

Let x be the number of ounces of chocolate chips in the first batch.

x + 2x + 1/2x = 36

Monica made a total of 98 cookies of three different flavors- chocolate chip, oatmeal raisin and peanut butter. The number of oatmeal raisin was twice the number of peanut butter. The number of chocolate chip was three times more than the number of oatmeal. How many of each type did Monica make?

Let x be the number of peanut butter cookies,

X + 2x + 3(2x) = 98

The PTO set up a buffet fundraiser at school at a total cost of $15 per person, with an extra cost for dessert. If a family of 5 all ate the buffet and dessert for a total of $90, what is the total cost of dessert?

Let x be the cost of dessert,

5 (15 + x) = 90

Ms. Nowakowski filled her gas tank completely before leave for LA. After she had driven 300 miles she discovered she still had a quarter tank left. How far can Ms. Nowakowski travel on a full tank?

Let x be the miles traveled on a full tank,

(3/4)x = 300

Ms. Nowakowski commuted to school and back from her house, two days this week. She commuted the other three days from her Mom’s house to school and then back. At the end of the week, she had driven 140 miles. If Ms. Nowakowski’s mom lives 10 miles closer to school than Ms. Nowakowski, how far is her daily commute?

Let x be the number of miles on Ms. Nowakowski’s daily commute,

2x + 3(x-10) = 140

Ellie got her test back from Ms. Nowakowski, she saw that Jonah’s score was ten points higher than her score and that Lev’s score was 7 points lower. If together they averaged a score of 89, what was Ellie’s score?

Let x be Ellie’s test score,

[X + (x + 10) + (x – 7)] / 3 = 89

Ms. Nowakowski’s class has some boys and some girls. There are 5 more girls than there are boys. If there are 25 students in the class, how many are boys?

Let x be the number of boys in class,

x + (x +5) = 25

There are a total of 20 students in Ms. Waldo’s elective, 6^th, 7^th and 8^th graders. If the number of 7^th graders is two more than the number of 6^th graders and the number of 8^th graders is one more than the number of 7^th graders, how many students of each grade are there?

Let x be the number of 6^th graders,

x + (x + 2) + (x + 2 + 1) = 20

Ms. Nowakowski decided to rent a car on her vacation. She can either rent a car for $35 day plus $0.40 a mile or for $20 a day plus $0.55 per mile. How many miles would Ms. Nowakowski have to drive for the two rental cars to cost the same amount?

Let x be the number of miles driven,

35 + 0.40x = 20 + 0.55x

Becca wants to paint a ceramic planter at a local potter shop. The total price of the planter is the cost of the planter plus the hourly painting rate of $6 an hour. How many hours did Becca paint if the planter cost $9 and she paid $33 for the total bill?

Let x be the number of hours Becca painted,

33 = 9 + 6x