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5.75 Solve Multi Step Word Problems Using Equations with an Unknown Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 5 Math worksheet provides structured practice on 5.75 Solve Multi Step Word Problems Using Equations with an Unknown. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Skill description: Select the correct equation that represents a multi-step word problem and identify the correct value of the unknown. Choose the step-by-step solution that follows the order of operations and uses grouping symbols correctly. Corresponding standards: CCSS 5.OA.A.2; CCSS MP4.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 5

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 5.75 Solve Multi Step Word Problems Using Equations with an Unknown skill assessments:

Problem 1Difficulty: Mastery

Wendy is counting gift bags. There are 5 bags with x + 4 items each and 2 bags with x + 12 items each. Altogether, there are 191 items. Which option shows a correct equation for the situation and correctly solves for x?

AEquation: 5*(x + 4) + 2 × x + 12 = 191 1) Expand: 5 × x + 20 + 2 × x + 12 = 191 2) Combine: 7 × x + 32 = 191 3) Subtract 32: 7 × x = 159 4) Divide by 7: x = 22 x = 22

BEquation: 5*(x + 4) + 2*(x + 12) = 191 1) Use distribution: 5*(x + 4) = 5 × x + 20, and 2*(x + 12) = 2 × x + 24 2) Add the expressions: 7 × x + 44 = 191 3) Subtract 44: 7 × x = 147 4) Divide by 7: x = 21 x = 21

CEquation: 5*(x + 4) + 2*(x − 12) = 191 1) Expand: 5 × x + 20 + 2 × x − 24 = 191 2) Combine: 7 × x + -4 = 191 3) Subtract -4: 7 × x = 195 4) Divide by 7: x = 27 x = 27

DEquation: 5*(x + 4) + 2*(x + 12) = 191 1) Expand and combine: 7 × x + 44 = 191 2) Subtract 44: 7 × x = 147 3) Divide by 7: x = 23 x = 23

Solution & Explanation:Expand both products, then combine. Solve 7x + 44 = 191. The solution is x = 21.

Problem 2Difficulty: Mastery

Victor is counting science bags. There are 6 bags with x + 1 supplies each and 4 bags with x + 9 supplies each. Altogether, there are 172 supplies. Which option shows a correct equation for the situation and correctly solves for x?

AEquation: 6*(x + 1) + 4 × x + 9 = 172 1) Expand: 6 × x + 6 + 4 × x + 9 = 172 2) Combine: 10 × x + 15 = 172 3) Subtract 15: 10 × x = 157 4) Divide by 10: x = 15 x = 15

BEquation: 6*(x + 1) + 4*(x − 9) = 172 1) Expand: 6 × x + 6 + 4 × x − 36 = 172 2) Combine: 10 × x + -30 = 172 3) Subtract -30: 10 × x = 202 4) Divide by 10: x = 20 x = 20

CEquation: 6*(x + 1) + 4*(x + 9) = 172 1) Expand and combine: 10 × x + 42 = 172 2) Subtract 42: 10 × x = 130 3) Divide by 10: x = 15 x = 15

DEquation: 6*(x + 1) + 4*(x + 9) = 172 1) Use distribution: 6*(x + 1) = 6 × x + 6, and 4*(x + 9) = 4 × x + 36 2) Add the expressions: 10 × x + 42 = 172 3) Subtract 42: 10 × x = 130 4) Divide by 10: x = 13 x = 13

Solution & Explanation:Expand both products, then combine. Solve 10x + 42 = 172. The solution is x = 13.

Problem 3Difficulty: Mastery

Uma is counting painting kits. There are 2 kits with x + 7 brushes each and 3 kits with x + 10 brushes each. Altogether, there are 154 brushes. Which option shows a correct equation for the situation and correctly solves for x?

AEquation: 2*(x + 7) + 3 × x + 10 = 154 1) Expand: 2 × x + 14 + 3 × x + 10 = 154 2) Combine: 5 × x + 24 = 154 3) Subtract 24: 5 × x = 130 4) Divide by 5: x = 26 x = 26

BEquation: 2*(x + 7) + 3*(x − 10) = 154 1) Expand: 2 × x + 14 + 3 × x − 30 = 154 2) Combine: 5 × x + -16 = 154 3) Subtract -16: 5 × x = 170 4) Divide by 5: x = 34 x = 34

CEquation: 2*(x + 7) + 3*(x + 10) = 154 1) Expand and combine: 5 × x + 44 = 154 2) Subtract 44: 5 × x = 110 3) Divide by 5: x = 24 x = 24

DEquation: 2*(x + 7) + 3*(x + 10) = 154 1) Use distribution: 2*(x + 7) = 2 × x + 14, and 3*(x + 10) = 3 × x + 30 2) Add the expressions: 5 × x + 44 = 154 3) Subtract 44: 5 × x = 110 4) Divide by 5: x = 22 x = 22

Solution & Explanation:Expand both products, then combine. Solve 5x + 44 = 154. The solution is x = 22.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 5 Math students. It aligns with educational standard 5.75 (Solve Multi-Step Word Problems Using Equations with an Unknown).