Algebra
3x - 15 = 18
3x = 33
x = 11
Simplify 3(x + 1) - 2 (x - 2 )
3(x + 1) - 2 (x - 2 )
3x + 3 - 2x + 4
x + 7
Combine like terms and simplify:
5x - (3x - 4)
Be careful with negative signs
5x - (3x - 4 ) =
5x - 3x + 4
2x + 4
Max has only quarters in his wallet. If the amount of money he has is $2.75, how many quarters does he have?
2.75 / 0.25 = 11 quarters
Simplify: (3x2)3
(3x2)3
(3x2) (3x2) (3x2)
27x6
David’s sister is 10 years less than double his age. If David is 25, how old is his sister?
S=2D-10
S=2(25)-10=50-10=40
S=40
Solve for x
3x2 - 4 = 44
3x2 - 4 = 44
3x2 = 48
x2 = 16
x = 4
The sum of x and 7 is equal to the quotient of x and 3. Find the value of x.
x+7=x/3
3(x+7)=x
3x+21=x
21=-2x
x=-10.5
What is (x + 2)2
(x+2)2 = (x+2)(x+2) = x2 + 2x + 2x + 4
x2 + 4x + 4
The sum of three consecutive multiples of 9 equals to 135. What is the middle value of the three consecutive multiples?
let x=1st multiple
let x+9=2nd multiple
let x + 18=3rd multiple
x+x+9+x+18=135
3x+27=135
3x=108
x=36
2nd multiple=45
A recipe for a protein shake says for every 2 tablespoons of protein powder add 2.5 cups of water. If you follow the recipe and use 5 tablespoons of protein powder, how many cups of water do you need?
2/2.5 = 5/x
cross multiply
2x=5(2.5)
2x=12.5
x=6.25 cups of water
The perimeter of a rectangle is 250 inches. The length is 3 inches more than the width. Find the dimensions of the rectangle.
Perimeter =2 length + 2 width
250=2(w+3)+2(w)
250=2w+6+2w
250=4w+6
244=4w
61=w
width=61 inches
length=64 inches
A laptop that originally costs $1500 is on sale at a discount of 10%. You decide to purchase the laptop and discover that there is a 5% sales tax. How much does the laptop cost after the tax?
1500(0.9)(1.05)=$1417.5
Three consecutive multiples of 5 have a sum equal to 3000. What is the largest of the three consecutive multiples?
let x = first multiple of 5
let x+5=second multiple
let x+10=third multiple
x+x+5+x+10=3000
3x+15=3000
3x=2985
x=995
largest = 995+10=1005
The quotient of 2x and 3 is equal to the difference of x and 5. Find the value of x
2x/3=x-5
2x=3(x-5)
2x=3x-15
-x=-15
x=15
The product of 3 and the sum of x and 10 is equal to 45. Find the value of x.
3(x+10)=45
3x+30=45
3x=15
x=5
Samantha and Zoey are hitting baseballs at a batting cage. Samantha and Zoey combined for a total of 40 hits. If Samantha hit 8 more baseballs than Zoey, how many baseballs did Zoey hit?
Let S = Samantha's number of hits
Let Z =Zoey's number of hits
S+Z=40
S=Z+8
Z+8+Z=40
2Z+8=40
2Z=32
Z=16
The square of the sum of b and 7 is equal to the square of the difference of b and 2. Find the value of b in its simplest form.
(b+7)2=(b-2)2
b2+14b+49=b2-4b+4
14b+49=-4b+4
18b=-45
b=-45/18=-5/2
Jenny and Lisa went to pick apples at an apple garden. They were able to pick 75 apples in 2 hours. How long would it take them to pick 300 apples together?
75 apples in 2 hours
150 apples in 4 hours
300 apples in 8 hours
ANS: 8 hours
Jacob has a younger sister that is currently one-third of his age. In 6 years, he will be double her age. How old is Jacob currently?
Let J = Jacob's current age, S=sister's current age
J=3S
J+6=2(S+6)
3S+6=2S+12
S=6
J=18
A pair of painters take 3 days to paint a house. They are trying to expand and want to hire one more painter. If they all paint at the same rate, how many days would it take three painters to paint 5 houses?
ANS: 10 days
2 painters -- 3 days -- 1 house = 6 days of work per house
1 painter -- 6 days -- 1 house
1 painter -- 30 days -- 5 houses
3 painters -- 10 days -- 5 houses
A square has an area of 36 ft2, what is the perimeter of the square in inches?
Area of a square=s2
36=s2
s=6 feet
perimeter square=4s
perimeter=46=24 feet
Perimeter in inches = 24 x 12 = 288 inches
(2x + 3) / 5 = (x - 1) / 3
3(2x + 3) = 5(x - 1)
6x + 9 = 5x - 5
x = - 14
Simplify: (((53)2)0
(((53)2)0 = 1
Anything to the 0 power equals 1
Evaluate the expression if x = 4: 5x3 - 0.5x2 - 12x - 1
5(4)3 - 0.5(4)2 - 12(4) - 1
5(64) - 0.5(16) - 48 - 1
320 - 8 - 48 - 1
263