Question

Translating and Solving Word Equations:

Translate then solve the algebraic equation for the following problems:

Fourteen less than 5 times a number is 1. Identify the integer.

When the sum of a number and 3 is subtracted from 10 the result is 5. Identify the integer.

The sum of two consecutive integers is 139. Find the integers.

The sum of two even consecutive integers is 46. Find the integers.

The sum of three consecutive integers is 57. Find the integers.

Answer 1

Solution:

(1) Let the number be x. Then, according to the statement

5x-14=1

adding 14 on both sides

5x-14+14=1+14

5x=15

divide both sides by 5

x=3

So, the integer is 3

(2)  Let the integer be x. Then, according to the statement,

10-(x+3)=5

10-x-3=5

7-x=5

subtracting 7 from both sides

7-x-7=5-7

-x=-2

OR

x=2

So, the integer is 2

(3) Let the first integer is x, then next consecutive integer=x+1. Now, according to the statement,

x+(x+1)=139

2x+1=139

subtracting 1 from both sides

2x+1-1=139-1

2x=138

dividing by 2 on both sides

x=69

So, the first integer is 69 and second integer is 69+1=70.

Hence, the integers are 69 and 70

(4) Let the first even integer is x. Then, next consecutive even integer will be x+2. Now, according to the statement,

x+(x+2)=46

x+x+2=46

2x+2=46

substracting 2 from both sides

2x+2-2=46-2

2x=44

dividing both sides by 2

x=22

So, the first even integer=22 and next consecutive even integer=22+2=24

Hence, the integers are 22 and 24

(5) Let the first integer=x, then next consecutive integer=x+1 and next to next consecutive integer=x+2.

Now, according to the statement,

x+(x+1)+(x+2)=57

x+x+1+x+2=57

2x+3=57

subtracting 3 from both sides

2x+3-3=57-3

2x=54

dividing both sides by 2

x=27

So, the first integer=27, Second integer=27+1=28 and third integer=27+2=29

Hence, the integers are 27, 28 and 29