An equation is a mathematical statement that two expressions have the same value, which are separated by an equal sign, “=”.
Example 1 :
The sum of three times a number x and 5 is 17. What is the number?
Solution :
3x + 5 = 17
Subtract 5 on both sides.
3x = 17-5
3x = 12
Divide by 3 on both sides.
x = 12/3
x = 4
Example 2 :
As a membership fee, a health club charges a one-time amount of $40 and charges $25 for each month. The total fee after m months is $240. What is the value of m?
Solution :
40 + 25m = 240
Subtract 40 on both sides.
25m = 240-40
25m = 200
Divide by 25 on both sides.
m = 200/25
m = 8
Example 3 :
A runner warms up for ten minutes and then takes seven minutes to run each mile. The total time after r miles is 45 minutes. How many miles are run?
Solution :
Time taken for warm up = 10 minutes
Time taken to run each mile = 7 minutes
Number of miles covered = r
10+7r = 45
Subtract 10 on both sides.
7r = 45-10
7r = 35
Divide by 7 on both sides.
r = 35/7
r = 5
Example 4 :
Jaimie picks out a blouse to purchase. It is on sale for 25% off plus she has got $10 off coupon. She pays $23 for the blouse. Determine the original price.
Solution :
Let x be the original price of coupon.
0.75x - 10 = 23
Add 10 on both sides.
0.75x = 23+10
0.75x = 33
Divide by 0.75 on both sides.
x = 33/0.75
x = 44
Example 5 :
Michael is collecting sea glass from the beach. He begins with 14 pieces in his collection and adds 3 new pieces per day. Determine how many days it will take Michael to have 80 pieces of sea glasses in his collection.
Solution :
Let x be the number of days he is collecting sea glass.
Number of glasses collected = 80
14 + 3x = 80
Subtract 14 on both sides.
3x = 80-14
3x = 66
Divide by 3 on both sides.
x = 66/3
x = 22
Example 6 :
Jacob joined a gym last year. His total bill for the year was $410 including a monthly membership fee and a one-time $50 enrollment fee.
Solution :
Let x be Jacob's monthly membership fee.
One time fee = $50.
Total bill = $410
12x + 50 = 410
Subtract 50 on both sides.
12x = 410-50
12x = 360
Divide by 12 on both sides.
x = 360/12
x = 30
Example 7 :
The cell phone company charges $44.95 a month and $0.25 per text message. The bill for the month is $60.45. How many texts (x) were sent?
Solution :
Let x be the number of text messages.
Bill amount = $60.45
Company charge = 44.95
Cost per text message = 0.25
44.95 + 0.25x = 60.45
Subtract 44.95 on both sides.
0.25x = 60.45-44.95
0.25x = 15.5
Divide by 0.25 on both sides.
x = 15.5/0.25
x = 62
Example 8 :
You pay $80 for a game system. The monthly rental fee for games is m dollars. Your cost for the year is $188. Using the equation 12m + 80 = 188, how much is your monthly fee?
a) $8 b) $9 c) $12 d) $22
Solution :
12m + 80 = 188
Subtracting 80 on both sides
12m = 188 - 80
12m = 108
m = 108/12
m = 9
Monthly rental fee is $9. So, option b is correct.
Example 9 :
You and your friend rent a tandem bike. Your total cost is $42. Write and solve an equation to find the number of extra hours you rented the bike.
Solution :
Total cost = $42
For three hours, the amount is $24
Let x be the extra number of hours. Charge for extra hours = $4.50
24 + 4.50x = 42
4.50x = 42 - 24
4.50x = 18
x = 18/4.50
x = 4
So, extra hours you rented the bike is 4.
Example 10 :
You and your friend rent a kayak. It costs $40 for the first 4 hours and $7.50 for each extra hour. Your total cost is $62.50. Write and solve an equation to find the number of extra hours you rented the kayak.
Solution :
Total cost = $62.50
For three hours, the amount is $40
Let x be the extra number of hours. Charge for extra hours = $7.50
40 + 7.50x = 62.50
7.50x = 62.50 - 40
7.50x = 22.5
x = 22.5/7.50
x = 3
So, extra hours you rented the kayak is 3.
Example 11 :
Why is the equation 5x − 12 = 23 called a two-step equation?
Solution :
Given equation is 5x − 12 = 23
Step 1 :
To solve this equation, we have to add 12 on both sides
5x = 23 + 12
5x = 35
Step 2 :
Dividing by 5 on both sides
x = 35/5
x = 7
Example 12 :
Describe and correct the error in solving the equation.
Solution :
Solving this equation,
4 = (y/8) + 1
Subtracting 1 on both sides
4 - 1 =(y/8)
3 = (y/8)
Multiplying by 8, we get
3(8) = y
y = 24
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM