Worksheets: word problemsEquations and inequalities · high school

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Answer key · group A · for the teacher · sheet no. 204 517

Word problems

1.3 cmx(x + 9) : 2 = 18 ;18 · 2 = 36, x(x + 9) = 36 ;x² + 9x − 36 = 0 ;9² − 4 · 1 · (−36) = 225

2.40 ptsx + 3x + 11 = 171 ;171 − 11 = 160 ;160 : 4 = 40

3.10x² = 6x + 40 ;x² − 6x − 40 = 0 ;(−6)² − 4 · 1 · (−40) = 196 ;14 · 14 = 196

4.7 cmx(x + 3) = 70 ;x² + 3x − 70 = 0 ;3² − 4 · 1 · (−70) = 289 ;17 · 17 = 289

5.30 ptsx + 3x + 6 = 126 ;126 − 6 = 120 ;120 : 4 = 30

Maths worksheets · phiboard.com

Answer key

Quiz

Word problems

GroupAB

Name Date Score / 18

1.In a right triangle one leg is 5 cm longer than the other, and the area of the triangle is 117 cm². Find the length of the shorter leg.(3 pt)

2.Adam and Mary scored 77 points together. Mary scored 20 more than 2 times what Adam scored. How many points did Adam score?(3 pt)

3.The sum of the squares of two consecutive natural numbers is 13. Find the smaller of these numbers.(3 pt)

4.One side of a square was lengthened by 2 cm and the other by 6 cm. The result is a rectangle with an area of 165 cm². Find the side length of the square.(3 pt)

Maths worksheets · phiboard.com

Group B

Quiz

Word problems

GroupAB

Name Date Score / 18

1.In a right triangle one leg is 9 cm longer than the other, and the area of the triangle is 18 cm². Find the length of the shorter leg.(3 pt)

2.Michael and Jacob scored 171 points together. Jacob scored 11 more than 3 times what Michael scored. How many points did Michael score?(3 pt)

3.The square of a certain positive number is 40 greater than the product of this number and 6. What is the number?(3 pt)

4.One side of a rectangle is 3 cm longer than the other, and the area of the rectangle is 70 cm². Find the length of the shorter side.(3 pt)

Maths worksheets · phiboard.com

Group A

Sheet settings

Quiz6 questions2 groups1 topic

Sheet no.204 517The number is only shown here and on the answer key - never on the student sheet. The same number with the same topics gives the same sheet.

answer key at the endall groups

Quiz

Word problems

GroupAB

Name Date Score / 18

1.In a right triangle one leg is 9 cm longer than the other, and the area of the triangle is 18 cm². Find the length of the shorter leg.(3 pt)

2.Michael and Jacob scored 171 points together. Jacob scored 11 more than 3 times what Michael scored. How many points did Michael score?(3 pt)

3.The square of a certain positive number is 40 greater than the product of this number and 6. What is the number?(3 pt)

4.One side of a rectangle is 3 cm longer than the other, and the area of the rectangle is 70 cm². Find the length of the shorter side.(3 pt)

5.Adam and Anna scored 126 points together. Anna scored 6 more than 3 times what Adam scored. How many points did Adam score?(3 pt)

6.The square of a certain positive number is 104 greater than the product of this number and 5. What is the number?(3 pt)

Maths worksheets · phiboard.compage 10 of 10

Answer key · group A · for the teacher · sheet no. 204 517

Word problems

1.3 cmx(x + 9) : 2 = 18 ;18 · 2 = 36, x(x + 9) = 36 ;x² + 9x − 36 = 0 ;9² − 4 · 1 · (−36) = 225

2.40 ptsx + 3x + 11 = 171 ;171 − 11 = 160 ;160 : 4 = 40

3.10x² = 6x + 40 ;x² − 6x − 40 = 0 ;(−6)² − 4 · 1 · (−40) = 196 ;14 · 14 = 196

4.7 cmx(x + 3) = 70 ;x² + 3x − 70 = 0 ;3² − 4 · 1 · (−70) = 289 ;17 · 17 = 289

5.30 ptsx + 3x + 6 = 126 ;126 − 6 = 120 ;120 : 4 = 30

6.13x² = 5x + 104 ;x² − 5x − 104 = 0 ;(−5)² − 4 · 1 · (−104) = 441 ;21 · 21 = 441

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

Quiz

Word problems

GroupAB

Name Date Score / 18

1.In a right triangle one leg is 5 cm longer than the other, and the area of the triangle is 117 cm². Find the length of the shorter leg.(3 pt)

2.Adam and Mary scored 77 points together. Mary scored 20 more than 2 times what Adam scored. How many points did Adam score?(3 pt)

3.The sum of the squares of two consecutive natural numbers is 13. Find the smaller of these numbers.(3 pt)

4.One side of a square was lengthened by 2 cm and the other by 6 cm. The result is a rectangle with an area of 165 cm². Find the side length of the square.(3 pt)

5.Mary and Philip scored 55 points together. Philip scored 1 more than 5 times what Mary scored. How many points did Mary score?(3 pt)

6.The sum of the squares of two consecutive natural numbers is 221. Find the smaller of these numbers.(3 pt)

Maths worksheets · phiboard.compage 10 of 10

Answer key · group B · for the teacher · sheet no. 204 517

Word problems

1.13 cmx(x + 5) : 2 = 117 ;117 · 2 = 234, x(x + 5) = 234 ;x² + 5x − 234 = 0 ;5² − 4 · 1 · (−234) = 961

2.19 ptsx + 2x + 20 = 77 ;77 − 20 = 57 ;57 : 3 = 19

3.2x² + (x + 1)² = 13 ;2x² + 2x + 1 = 13, 2x² + 2x − 12 = 0, x² + x − 6 = 0 ;1² − 4 · 1 · (−6) = 25 ;5 · 5 = 25

4.9 cm(x + 2)(x + 6) = 165 ;x² + 8x + 12 = 165, x² + 8x − 153 = 0 ;8² − 4 · 1 · (−153) = 676 ;26 · 26 = 676

5.9 ptsx + 5x + 1 = 55 ;55 − 1 = 54 ;54 : 6 = 9

6.10x² + (x + 1)² = 221 ;2x² + 2x + 1 = 221, 2x² + 2x − 220 = 0, x² + x − 110 = 0 ;1² − 4 · 1 · (−110) = 441 ;21 · 21 = 441

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

What goes on the sheet: word problems

The generator draws questions from 3 question types in this topic. Every quiz group gets the same types in the same order, only with different numbers, and a practice sheet goes from easier to harder.

Word problems with equations
Word problems with quadratic equations - area of a shape
Word problems with quadratic equations - finding a number

What the section covers in the curriculum: linear equations (including contradictions and identities), linear inequalities, quadratic equations and inequalities, factored polynomial equations, simple rational equations, word problems leading to equations

Students can also practise online - the same question types, with step-by-step solutions: Exercises: word problems →

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