Free Printable AQR 1.3 Assignment Problem Solving Equations

1.

Write an equation or inequality that represents the scenario and solve.

Five less than twice a number is 18.

What is the number?

a)

$2x-5=18$

x=11.5

b)

$5-2x=18$

x=6.5

c)

$2x-5=18$

x=-11.5

d)

$5-2x=18$

x=-6.5

2.

The perimeter of a triangle is 52 inches.

The first side of the triangle is 7 inches longer than the second side.

The third side is 3 inches shorter than the second side.

Write an equation to represent this scenario and find the length of each side.

a)

$52=\left(x+7\right)+\left(x\right)+\left(x-3\right)$

16", 23", 13"

b)

$52=x+x+x$

17.33", 17.33", 17.33"

c)

$52=\left(x+7\right)+\left(x-3\right)$

24", 31", 21"

d)

$52=x+7-3$

48", 55", 45"

3.

The sum of three consecutive integers is 249.

Write an equation to represent this scenario then find the integers.

a)

$\left(x\right)+\left(x+1\right)+\left(x+2\right)=249$

82, 83, 84

b)

$x+x+x=249$

83, 83, 83

c)

$x^3=249$

6.29, 6.29, 6.29

4.

Write an equation that represents the scenario and solve.

When six is subtracted from half of a number, the result is 18.

What is the number?

a)

$\frac{1}{2}x-6=18$

x=48

b)

$6-\frac{1}{2}x=18$

x=-24

c)

$\frac{1}{2}x-6=18$

x=24

d)

$6-\frac{1}{2}x=18$

x=-48

5.

The sum of two consecutive integers is 59.

Write an equation to represent this scenario then find the integers.

a)

$\left(x\right)+\left(x+1\right)=59$

29, 30

b)

$x+x=59$

29.5, 29.5

c)

$x^2=59$

7.68, 7.68

6.

In 2008, Pierre’s Pizza and Burger Palace together had revenue totaling $470,000.

Burger Palace took in $90,000 less than Pierre’s Pizza.

Write and solve an equation to determine how much each restaurant earned in revenue.

a)

$470,000=\left(x\right)+\left(x-90,000\right)$

P.P.: $280,000; B.P.: $190,000

b)

$470,000=\left(x\right)+\left(x-90,000\right)$

P.P.: $190,000; B.P.: $280,000

c)

$470,000=x-90,000$

P.P.: $560,000: B.P.: $380,000

d)

$x\ =\ 470,000-90,000$

P.P.: $380,000; B.P.: $290,000

7.

The perimeter of a triangle is 37 feet.

The first side of the triangle is 2 feet longer than the second side.

The third side is 5 feet longer than the second side.

Write an equation to represent this scenario and find the length of each side.

a)

$37=\left(x+2\right)+\left(x\right)+\left(x+5\right)$

10 ft, 12 ft, 15 ft

b)

$37=x+x+x$

12.33 ft, 14.33 ft, 17.33 ft

c)

$37=\left(x+2\right)+\left(x+5\right)$

15 ft, 17 ft, 20 ft

d)

$37=x+2+5$

30 ft, 32 ft, 35 ft

8.

When the lesser of two consecutive odd integers is added to twice the greater, the result is 187.

Write and equation to represent this scenario and find the integers

a)

$\left(x\right)+2\left(x+2\right)=187$

x=61

x+2=63

b)

$\left(x\right)+2\left(x+2\right)=187$

x=61.67

x+2=63.67

c)

$\left(x\right)+\left(2x\right)=187$

x=62.33

2x=124.67

d)

$\left(x\right)+\left(x+2\right)=187$

x=92.5

x+2=94.5

9.

An irregular hexagon has sides that are consecutive integers. The Perimeter of the hexagon is 117 mm.

Write an equation to represent this scenario and determine the lengths of the shortest and the longest sides.

a)

$\left(x\right)+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)+\left(x+5\right)=117$ $shortest\ =\ 17mm$ $longest\ =\ 22mm$

b)

$\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)+\left(x+5\right)+\left(x+6\right)=117$ $shortest=17.83mm$ $longest\ =\ 22.83mm$

c)

$6x=117$

shortest\ =\ 19.5mm

longest\ =\ 25.5mm

d)

$x+6=117$

Shortest\ =\ 111mm

longest\ =\ 111mm

AQR 1.3 Assignment Problem Solving Equations

Total questions: 9

Worksheet time: 17mins

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