# 3.2 Solve percent applications

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By the end of this section, you will be able to:
• Translate and solve basic percent equations
• Solve percent applications
• Find percent increase and percent decrease
• Solve simple interest applications
• Solve applications with discount or mark-up

Before you get started, take this readiness quiz.

1. Convert 4.5% to a decimal.
If you missed this problem, review [link] .
2. Convert 0.6 to a percent.
If you missed this problem, review [link] .
3. Round 0.875 to the nearest hundredth.
If you missed this problem, review [link] .
4. Multiply (4.5)(2.38).
If you missed this problem, review [link] .
5. Solve $3.5=0.7n.$
If you missed this problem, review [link] .
6. Subtract $50-37.45.$
If you missed this problem, review [link] .

## Translate and solve basic percent equations

We will solve percent equations using the methods we used to solve equations with fractions or decimals. Without the tools of algebra, the best method available to solve percent problems was by setting them up as proportions. Now as an algebra student, you can just translate English sentences into algebraic equations and then solve the equations.

We can use any letter you like as a variable, but it is a good idea to choose a letter that will remind us of what you are looking for. We must be sure to change the given percent to a decimal when we put it in the equation.

Translate and solve: What number is 35% of 90?

## Solution

 Translate into algebra. Let $n$ = the number. Remember "of" means multiply, "is" means equals. Multiply. $31.5$ is $35%$ of $90$

Translate and solve:

What number is 45% of 80?

36

Translate and solve:

What number is 55% of 60?

33

We must be very careful when we translate the words in the next example. The unknown quantity will not be isolated at first, like it was in [link] . We will again use direct translation to write the equation.

Translate and solve: 6.5% of what number is $1.17? ## Solution  Translate. Let $n=$ the number. Multiply. Divide both sides by 0.065 and simplify. $6.5%$ of $18$ is $1.17$ Translate and solve: 7.5% of what number is$1.95?

$26 Translate and solve: 8.5% of what number is$3.06?

$36 In the next example, we are looking for the percent. Translate and solve: 144 is what percent of 96? ## Solution  Translate into algebra. Let $p=$ the percent. Multiply. Divide by 96 and simplify. Convert to percent. $144$ is $150%$ of $96$ Note that we are asked to find percent, so we must have our final result in percent form. Translate and solve: 110 is what percent of 88? 125% Translate and solve: 126 is what percent of 72? 175% ## Solve applications of percent Many applications of percent —such as tips, sales tax, discounts, and interest—occur in our daily lives. To solve these applications we’ll translate to a basic percent equation, just like those we solved in previous examples. Once we translate the sentence into a percent equation, we know how to solve it. We will restate the problem solving strategy we used earlier for easy reference. ## Use a problem-solving strategy to solve an application. 1. Read the problem. Make sure all the words and ideas are understood. 2. Identify what we are looking for. 3. Name what we are looking for. Choose a variable to represent that quantity. 4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation. 5. Solve the equation using good algebra techniques. 6. Check the answer in the problem and make sure it makes sense. 7. Answer the question with a complete sentence. #### Questions & Answers hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused. Alicia Reply what do you need help in? Felix subtracting a negative....is adding!! Heather look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number... Felix for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer... Felix —12 Niazmohammad Thanks Felix.l also get confused with signs. Esther Thank you for this Shatey Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles John Reply 168.50=R Heather john is 5years older than wanjiru.the sum of their years is27years.what is the age of each achol Reply 46 mustee j 17 w 11 Joseph john is 16. wanjiru is 11. Felix 27-5=22 22÷2=11 11+5=16 Joyce where's the answers? Ed Reply I don't see where the answers are. Ed Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart? Maddy Reply 3 Christopher 18t+14t=96 32t=96 32/96 3 Christopher show that a^n-b^2n is divisible by a-b Florence Reply What does 3 times your weight right now Cherokee Reply Use algebra to combine 39×5 and the half sum of travel of 59+30 Cherokee What is the segment of 13? Explain Cherokee my weight is 49. So 3 times is 147 Cherokee kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps tyler How to convert grams to pounds? paul What is the lcm of 340 Kendra Reply Yes Cherokee How many numbers each equal to y must be taken to make 15xy Malik Reply 15x Martin 15x Asamoah 15x Hugo 1y Tom 1y x 15y Tom find the equation whose roots are 1 and 2 Adda Reply (x - 2)(x -1)=0 so equation is x^2-x+2=0 Ranu I believe it's x^2-3x+2 NerdNamedGerg because the X's multiply by the -2 and the -1 and than combine like terms NerdNamedGerg find the equation whose roots are -1 and 4 Adda Ans = ×^2-3×+2 Gee find the equation whose roots are -2 and -1 Adda (×+1)(×-4) = x^2-3×-4 Gee yeah Asamoah Quadratic equations involving factorization Winner Reply there's a chatting option in the app wow Nana That's cool cool Nana Nice to meet you all Nana you too. Joan 😃 Nana Hey you all there are several Free Apps that can really help you to better solve type Equations. Debra Debra, which apps specifically. ..? Nana am having a course in elementary algebra ,any recommendations ? samuel Samuel Addai, me too at ucc elementary algebra as part of my core subjects in science Nana me too as part of my core subjects in R M E Ken at ABETIFI COLLEGE OF EDUCATION Ken ok great. Good to know. Joan 5x + 1/3= 2x + 1/2 sanam Plz solve this sanam 5x - 3x = 1/2 - 1/3 2x = 1/6 x = 1/12 Ranu Thks ranu sanam Please help me solve this 10x+14=-2x+38 Erica the previous equation should be 3x = 1/6 x=1/18 Sriram for the new one 10x + 2x = 38 - 14 Sriram 12x = 24 x=2 Sriram 10x + 14 = -2x +38 10x + 2x = 38 - 14 12x = 24 divide both sides by the coefficient of x, which is 12 therefore × = 2 vida a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions vinaya Reply a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs$6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs$5.71 per gallon?
(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
really
Asamoah
4x-7y=8 2x-7y=1 what is the answer?
x=7/2 & y=6/7
Pbp
x=7/2 & y=6/7 use Elimination
Debra
true
bismark
factoriz e
usman
4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2
Peggie
Frank
thanks
Ramil
x=7/2 y=6/7
Asamoah
Thanks , all of you are correct.
Joseph