Writing, Creating, and Solving Equations
Equation – A mathematical sentence that contains the equal sign.
By replacing certain words with mathematical symbols, you can rewrite the sentence into a mathematical sentence. Then just solve the equation to get your answer.
Key Words TranslationReplace with this Symbol
Ofmeans to multiplyreplace with an “x”
Ismeans equalsreplace with an = sign
Whatis the answer to the problemreplace with a variable (n)
What numberis the answer to the problemreplace with a variable (n)
What percentis the answer to the problemreplace with a variable (n)
Examples:What is 66 2/3% of 12?What is 30% of 150?
N = 66 2/3% x 12n = 30% x 150
N = 2/3 x 12n = 0.3 x 150
N = 8n = 45
40% of 60 is what number?What is 10 ½% of 70?
40% x 60 = nn = 10 ½% x 70
0.4 x 60 = nn = 0.105 x 70
n = 24n = 7.35
320 is 4000% of what number?42 is 66 2/3% of what number?
320 = 4000% x n42 = 66 2/3% x n
320 = 40 x n42 = 2/3 x n
n = 8n = 63
12 is 30% of what number?15 is 120% of what number?
12 = 30% x n15 = 120% x n
12 = 0.3 x n15 = 1.2 x n
n = 40 n = 12.5
What percent of 12 is 3?What percent of 15 is 3?
N x 12 = 3n x 15 = 3
N = 3 / 12n = 3 / 15
N = .25 = 25%n = .2 = 20%
What percent of 4 is 640?20 is what percent of 40?
N x 4 = 64020 = n x 40
N = 640 / 4n = 20 / 40
N = 160 = 16000%n = .5 = 50%
Solving Word Problems:
- Theresa made 11 of 20 free throws at basketball practice. What percent did she make?
(Convert the number of free throws made out of the total number of free throws attempted into a fraction, then convert that fractional answer into a percent.)
11 / 20 = 55 / 100 = 55%OR11 / 20 = .55 = 55%
- An article of clothing regularly selling for $78.62 is advertised at 10% off. Find the sale price.
(First find what 10% of the regular price which is $78.62. Then take that answer, which is the 10% off or discount on the clothing, and subtract it from the regular price of $78.62. This will give you the sale price of the clothing.)
78.62 x 10%= 78.62 x 0.1 = $7.86(discount on the clothing)
78.62 - 7.86 = $70.76(this is the sale price of the clothing)
Final Answer: $70.76
- A ski club planned a trip to Squaw Valley and 24 of the members signed up to go. If this is 40% of the club, how many total members does the ski club have?
(Since you do not know how many members are in the ski club and that is what the question is asking for, you make that your variable. We know that 24 members signed up which is a smaller number than are in the club and we know that 40% of the members in the club signed up for the trip; therefore, we can figure out the answer by taking 40% of (or times) the members in the club and setting it equal to the number of members going on the trip (24).)
40% x n = 24
0.4x n = 24
n = 24 / 0.4
n = 60Therefore, the answer is 60.
Examples:
1.The sum of 8 and 5 times a number is 43. Write an equation that can be used to find the unknown number?
2.A secretary at the police department makes $8 less per hour than the dispatcher. The combined hourly wage of the secretary and the dispatcher is $40.
3.The perimeter of a rectangle is 48 in. If the length is twice the width, what is the length of the rectangle?
4.A magazine sales person earns $250 a week plus a commission of of the total sales. If the total sales for the week were $693, what is the total that the sales person earned?
5.The sum of three consecutive integers is 81. What is the largest integer?
6.A 180 ft long board is cut into 3 pieces. The second piece of board is twice as long as the first. The third piece of board is six times as long as the first.
What is the length of the first piece of the board?
7.Jim wanted to know the age of his math teacher, Ms. Greenberg. The teacher said that if he added 28 to her age and then doubled it, the total would be 120.
How old is Jim's teacher?
8.The difference of 5 times a number and 8 is 27. Write an equation that can be used to find the unknown number?
9.The length of a swimming pool is 22 ft. The width is 40 ft. If the volume of the pool is 2,500 ft³, write an equation that could be used to find the depth of the pool?
10.Marcos drove twice as far as Candice. Together, they drove 66 miles. Write an equation that can be used to find the number of miles Candice drove?