Linear Equation Word Problems Worksheet

**Page 1**

1.

a. | 20 | ||

b. | 30 | ||

c. | 25 | ||

d. | 50 |

Height of the plant B is 20 ft, whose rate of growth is

Let both the plants will have the same height after

So, height of plant A after

25 + 2(

[Algebraic model.]

[Simplify.]

[Solve for

The plants will have the same height in 25 weeks.

Correct answer : (3)

2.

The front page of a newspaper is $12\frac{1}{2}$ inches wide. The left and right margins are each $x$ inches wide. The news is in four columns each of width 2 inches and the space between two columns is $\frac{1}{2}$ inch. Find the value of $x$.

a. | 2 | ||

b. | 3 | ||

c. | 1.5 | ||

d. | 1 |

Width of the newspaper =

Left, right margins are each of

The news is in four columns each of width 2 inches and the space between the two columns is

Now the front page of the newspaper can be seen as shown.

From the figure, we have

[Algebraic model.]

2

2

[Solve for

The value of

Correct answer : (3)

3.

Ethan has two cars A and B. He used car A on the first day of the week and car B on the next day. He drove car A at 45 miles per hour for 3 hours and car B at 49 miles per hour for 4 hours. What is the total distance traveled by Ethan in these two days?

a. | 135 miles | ||

b. | 61 miles | ||

c. | 331 miles | ||

d. | 196 miles |

Distance traveled by Ethan by the car A = (45)(3) = 135 miles.

[Distance = speed × time.]

Ethan drove the car B at 49 miles per hour for 4 hours.

Distance traveled by Ethan by the car B = (49)(4) = 196 miles.

[Distance = speed × time.]

So, the total distance traveled by Ethan = 135 + 196 = 331 miles.

Correct answer : (3)

4.

Brian has $1,500 and his sister Quincy has $1,920. Each gets $10 as an allowance per week. Brian saves his allowance and Quincy spends her allowance plus $20 each week. In how many weeks will they have equal amount with them?

a. | 342 weeks | ||

b. | 42 weeks | ||

c. | 14 weeks | ||

d. | 390 weeks |

Brian adds $10 each week to his amount and Quincy spends $20 (She gets $10 every week and spends it along with another $20) each week from her amount.

Let after

[Algebraic model.]

[Solve for

Brian and Quincy will have the same amount with them after 14 weeks.

Correct answer : (3)

5.

The number of students opting for Japanese and French in a school are 60 and 281 respectively. The number of students opting for Japanese has been increasing at the rate of 6 students per year and that for French has been decreasing at the rate of 11 students per year. How long will it take for the number of students taking Japanese to equal the number of students taking French?

a. | 2 years | ||

b. | 24 years | ||

c. | 26 years | ||

d. | 13 years |

The number of students who opted for French = 281 and the rate of decrease of students who opted French = 11 per year

Let after

The number of students who opted for Japanese after

[Increases at 6 students per year.]

The number of students who opted for French after

[Decreases at 11 students per year.]

60 + 6

[Algebraic model.]

17

[Solve for

After 13 years, the number of students opting for Japanese will be equal to the number of students opting for French.

Correct answer : (4)

6.

Brian wants to mail a packet. He packed it in a rectangular box as shown, which just meets the postal regulations. According to the postal regulations the combined length and girth of the package should not exceed 72 cm. If the length($l$) of the box is 28 cm, then what is the width of the box?

[Out of the three dimensions of a box the longest dimension is considered to be the length. The other two dimensions are each doubled and then added together to obtain the girth.]

[Out of the three dimensions of a box the longest dimension is considered to be the length. The other two dimensions are each doubled and then added together to obtain the girth.]

a. | 22 cm | ||

b. | 11 cm | ||

c. | 44 cm | ||

d. | 3 cm |

Length of the required box =

Girth of the box + Length of the box = 72 cm

[The box just meets the regulations.]

4

[The girth is the distance around the box.]

4

So, the width of the box is 11 cm.

Correct answer : (2)

7.

At West High University, 1430 students major in arts and 910 major in science. Arts students have been increasing at the rate of 40 students per year and the science students have been decreasing at the rate of 30 students per year. At these rates, after how many years the number of students who major in arts will be 3 times the number of students who major in science?

a. | 11 years | ||

b. | 9 years | ||

c. | 12 years | ||

d. | 10 years |

and rate of increase of students who major in Arts = 40 students per year

Number of students who major in Science = 910

and the rate of decrease of students who major in Science = 30 students per year

Let

[Algebraic model.]

[Solve for

After 10 years the number of students major in Arts will be 3 times the number of students major in Science.

Correct answer : (4)

8.

Andrew traveled on a bike at a speed of 70 miles per hour and traveled in a car at a speed of 300 miles per hour. His time of traveling on the bike is twice as the time of traveling in the car. If the total distance traveled was 1760 miles, then how many hours did Andrew travel on the bike?

a. | 4 hours | ||

b. | 510 hours | ||

c. | 2.63 hours | ||

d. | 8 hours |

The speed of the car in which Andrew traveled is 300 miles per hour.

Let

So, the distance traveled on the bike = (70)(2

The distance traveled by the car = (300)

So, the total distance traveled = (70)2

(70)2

[Total distance = 1760 miles.]

440

[Solve for

So, Andrew traveled on the bike for 8 hours.

[2

Correct answer : (4)

9.

Matt has $3,000 and adds $10 each week to it. Tommy has $4,040 and spends $30 from it each week. After how many weeks will both Matt and Tommy have the same amount with them?

a. | 26 weeks | ||

b. | 28 weeks | ||

c. | 33 weeks | ||

d. | 24 weeks |

The initial amount with Tommy = $4,040 and he spends $30 from it each week.

Let both Matt, Tommy will have the same amount after

After

[Matt increases his amount by $10 every week and Tommy decreases his amount by $30 every week.]

3000 + 10

[After

40

[Solve for

So, after 26 weeks both Matt, Tommy will have the same amount with them.

Correct answer : (1)

10.

The girth of a rectangular box of length 40 in., height 30 in. is 100 in.. What is the width of the box?

[Out of the three dimensions of a box the longest dimension is considered to be the length. The other two dimensions are each doubled and then added together to obtain the girth.]

[Out of the three dimensions of a box the longest dimension is considered to be the length. The other two dimensions are each doubled and then added together to obtain the girth.]

a. | 10 in. | ||

b. | 40 in. | ||

c. | 20 in. | ||

d. | 100 in. |

The girth of a rectangular box of length

[Definition.]

Height of the box is

2

2

[Substitute

[Solve for

So, the width of the box is 20 in..

Correct answer : (3)