Applications of Linear Equations

Question 1

If you have a text task and have to get out the variables for a linear equation, how do you do?

Tim earned 325 more in May than he did in April. Combined, she earned a total of 2825 for the two months. What were her earnings for the two month?

Answer 1

2825= x+x+325
….
….

Question 2

The sum of three CONSECUTIVE integers is 75. What are the numbers?

Answer 2

x
x+1
x+2

75=x+x+1+x+2
x=24

24,25,26

Question 3

If you have such a text task, what does … is … indicate

Answer 3

a = sign in the equation

Question 4

The length of a rectangular field is 10 less than 3 times the width. If the perimeter is 860, find the length and width.

Answer 4

L=3w-10
Perimeter Formula= 2W+2L
860=2W+2(3W-10)
W=110
L=3*110-10=320
320*2+110*2=860

Question 5

Note the Formula of the percent equation.

45 is what percentage of 180?

Answer 5

amount= %(base)
Put x in depending what you need, amount percent or base.
Remember to put the % as decimal!

45=x(180) |:180
45/180=x
.25=x

Question 6

Simple interest:

How much money must be invested at 4% simple interest to have 3000 after 6 years?

Answer 6

Interest=Prt # principal(what you invest), rate(), time(). Interest means what you earn.
Total= P+Prt

2419,35

Question 7

After 6% of tax are added, the total amount of a television is 763,20. What was the original price?

Answer 7

x+0,06x=763,20

1,06x= …

Question 8

How many mL of a 5% saline solution must be mixed with 30mL of a 18% saline solution to create a 10% saline solution?

Answer 8

x0,05+300,18=0,1(x+30) | we need Ml on both sides so (x+30)
relook under mixture problems

Question 9

What is the formula to calculate the distance in a certain time?

Answer 9

D=rt # rate times time

Question 10

Transitive property:

A commuter train travels 20% faster than a cargo train. It takes the commuter train 2 hours to travel the route, the cargo train needs 3. Find the speed of each train.

Answer 10

Take D=rt for both

D=(x+20)2 and D=x(3) #if now both D are the same, we can set the equations next to each other.

(x+20)2 =x(3)