WORD PROBLEMS ON LINEAR EQUATIONS EOG 8TH GRADE

Problem 1 :

Which equation is equivalent to 2(3x - 1) = 14 - x?

a)   6x - 2 - x = 14        b) 6x - 1 + x = 14

c)  2(3x - 1) - x = 14     d) 6x - 2 + x = 14

Solution :

2(3x - 1) = 14 - x

6x - 2 = 14 - x

6x + x - 2 = 14

So, option d is correct.

Problem 2 :

A bakery sells bagels for $1.20 each and muffins for $1.50 each. Jane spent a total of $23.40 on bagels and muffins. If she bought 18 bagels and muffins combined, which equation can be used to find the number of bagels Jane bought?

A)  23.40 = 1.20(18 - b) + 1.50(b)

B)  23.40 = 1.20(18 - b) - 1.50(b)

C)  23.40 = 1.20(b) - 1.50(18 - b)

D)  23.40 = 1.20(b) + 1.50(18 - b)

Solution :

Cost of each bagel = $1.20

Cost of each muffin = $1.50

Let b the number of bagels.

Total number of bagel and muffins = 18

Total number of muffins = 18 - b

Total amount spent = $23.40

1.20b + 1.50(18 - b) = 23.40

So, option D is correct.

Problem 3 :

Which of the following expressions is equivalent to

x + 4(2x - 3y), when x = 3?

A) 27 - 3y      B) 11 - 3y     C) 27 - 12y     D) -9

Solution :

= x + 4(2x - 3y)

When x = 3

= 3 + 4(2(3) - 3y)

= 3 + 4(6 - 3y)

= 3 + 24 - 12y

= 27 - 12y

So, option C is correct.

Problem 4 :

The diagram below shows the McCray’s original rectangular patio and new square addition.

Which of the following expressions could be used to represent the area, in square yards, of the combined patios? 

a)  l(l + 5)        b)  l² + 5        c)  5l + l   d)  (l + 5)(l - 2)

Solution :

The shape which is at the top is square, at the bottom is rectangle.

Area of square = l²

Area of rectangle = l x 5

Total area = l² + l x 5

Problem 5 :

Which statement best describes the similarities of the graphs

2y = 7x + 1/3 and 2y = -3x + 1/3 ?

a) The lines are parallel

b)  The y-intercepts are the same.

c)  The x-intercepts are the same.

d)  The lines are perpendicular.

Solution :

2y = 7x + 1/3 -----(1)

y = (7/2) x + 1/6

Slope = 7/2 and y-intercept = 1/6

2y = -3x + 1/3 ------(2)

y = (-3/2)x + 1/6

Slope = -3/2 and y -intercept = 1/6

y-intercepts are same. So, option b is correct.

Problem 6 :

The Guilford County Greenway bike trail is a 16-mile trail system. The table below shows how far Jose had ridden along the trail at 5-minute intervals.

Which of the following equations expresses the relationship between time in minutes, x, and distance, y?

a) y = (3.2) (x/5)      b) y = (3.2)(x - 4)

c) y = 3.2x - 4          d) y = 5x + 3.2

Solution :

Choosing two points from the table,

(5, 3.2) and (10, 6.4)

Slope (m) = (6.4 - 3.2)/(10 - 5)

= 3.2/5

Equation of the line :

(y - y₁) = m(x - x₁)

slope (m) = 3.2/5 and (5, 3.2)

y - 3.2 = (3.2/5)(x - 5)

y = (3.2/5)(x - 5) + 3.2

y = (3.2/5)x - 3.2 + 3.2

y = (3.2/5)x

Problem 7 :

The following equation represents the amount of allowance (in dollars) Tanisha earns, y, for doing x chores during the week

y = x + 0.5

Which of the following ordered pairs is not a solution to the equation?

a) (2, $2.50)     b) (3, $3.00)    c) (4, $4.50)   d) (10, $10.50)

Solution :

y = x + 0.5

So, option b is correct answer.

Problem 8 :

One day, Enrico counts 10 cats in a pet store. Some of the cats have 5 toes on each front paw and 4 toes on each back paw. The rest of the cats are polydactyl, with 6 toes on each front paw and 4 toes on each back paw. All of the cats have 2 front paws and 2 back paws. If Enrico counts a total of 188 toes, how many of the cats are polydactyl?

a) 4      b)  5      c)  6     d)  10

Solution :

Let x be the some of the cats each has 5 toes on front paw and 4 toes in back paw.

Then 10 - x be the number of cats that are polydactyl.

Each cat will have 2 front paws and 2 back paws.

10x + 12(10 - x) + 8x + 8(10 - x) = 188

10x + 120 - 12x + 8x + 80 - 8x = 188

-2x + 200 = 188

-2x = -12

x = 6

Then 10 - x will be 4.

So, the number of cats that are polydactyl is 4.

Problem 9 :

Raoul is considering two plans offered by a music download service.

Plan A charges a monthly fee of $6.00 plus $0.95 per song n.

Plan B has no monthly fee and charges $1.20 per song n.

Which equation represents the total monthly cost c for plan A?

a) c = 6.95n    b) c = 5.95n    c)  c = 0.95n + 6

d) c = 1.20n + 6

Solution :

Number of songs to be downloaded = n

Monthly charge = 6, cost per song = 0.95

6 + 0.95n = c

So, option c is correct.

Problem 10 :

The table below shows the number  of hours Cassandra has spent babysitting for the past four weeks. What is the minimum number of hours she must babysit next week to have an average of 12 hours babysitting per week over the
five-week period?

a) 12 hours        b) 14 hours      c) 16 hours      d) 18 hours

Solution :

Average = 12 hours

Let x be the required number of hours.

(12 + 16 + 10 + 8 + x)/5 = 12

46 + x = 12(5)

46 + x = 60

x = 60 - 46

x = 14

So, option b is correct.

Problem 11 :

To make the costumes for the school play, the costume committee needs to buy 2  5/8 yards of ribbon for each of 3 costumes. How much money do they need for the ribbon?

a)  $7.50     b) $8.28     c) $9.84   d) $11.25

Solution :

Quantity of ribbon need to buy for 1 costume = 2  5/8 yards

Quantity of ribbon for 3 costumes = 3 (2  5/8)

Cost per yard = $1.25

Total cost = 3 (2  5/8) (1.25)

= $9.84

So, option c is correct.