I need some math help?

Solve the following problems:

1.

a) On Wednesday, Harry sold 3 times as many candy bars as on Tuesday. On Thursday, he sold 5 times as many bars as on Wednesday. He sold a total of 152 candy bars. How many did he sell each day?

b) Bill has 5 times as many baseball cards as Fred. Tim has 3 fewer than 4 times as many baseball cards as Fred. In all they have 167 baseball cards. How many does each have?

2.

a) The length of a rectangle is 5 more than the width. The perimeter of the rectangle is 168 inches. Find the dimensions of the rectangle.

b) The length of a rectangle is twice the width. If the length is increased by 4 inches and the width is diminished by 1 inch, a new rectangle is formed whose perimeter is 198 inches. Fine the dimensions of the original rectangle.

3.

a) John is now 3 times as old as his brother Sam. In 5 years, John will be twice as old as Sam will be then. Find their present ages.

b) Find four consecutive integers such that the sum of the second and the fourth is 132.

4.

a) Find four consecutive even integers such that twice the sum of the second and third exceeds 3 times the first by 34.

b) The difference between two numbers is 24. Find the numbers if their sum is 88.

5.

a) Separate 60 into two parts so that 3 times the smaller added to 6 more than 6 times the smaller = 60.

b) A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of:

Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.

(1) 50 mph (2) 70 mph (3) x mph

(4) (x + 10)mph (5) (x - 5)mph

*THANKS IN ADVANCE*

2 Answers

Relevance
  • 7 years ago
    Favorite Answer

    1-

    a:

    Let's assume the amount he sold on Tuesday is x , that means Wednesday is 3x and Thursday is 3x*5 = 15x.

    If the total amount of a candy he sold is 152 we can solve for x

    x+3x+15x=152

    19x=152

    Divide both sides by 19

    x=8

    That means he sold 8 candies On Tuesday,24 on Wednesday,120 on Thursday

    Add those up

    8+24=120=152

    The answer is correct

    ------------------------------------------------------------------------------------------------------------------------------ b: Assuming Fred has x baseball cards , Bill has 5x baseball cards , and Tim has 4x-3 baseball cards

    If the total amount of baseball cards is 167 we can solve for x

    x+5x+4x-3=167

    10x-3=167

    We move 3 to the right hand side of the equation

    10x=170

    We divide both sides by 10

    x=17

    That means Fred has 17 Baseball cards , Bill 85 . and Tim 65

    We add those up

    17+85+65=167

    The answer is correct

    ------------------------------------------------------------------------------------------------------------------------------

    2-

    a:

    Let the width be x , Therefore the length is 5x

    If the parameter is 168 inches we can solve for x

    2(x+5x)=168

    We distribute 2 (Distributive property)

    2x+10x=168

    12x=168

    We divide both sides by 12

    x=14

    That means the width of the rectangle is 14 and the length is 70.

    Checking

    (14+70)*2=84*2=168

    The answer is correct

    ------------------------------------------------------------------------------------------------------------------------------

    b:

    Let the width be x , Therefore the length is 2x

    We know if we increase the length by 4 inches and decrease the width by 1 inch the parameter is 198 inches

    We can solve for x

    2((x-1)+(2x+4))=198

    2(3x-3)= 198

    Distributing 2

    6x-6=198

    We move 6 to the right hand side of the equation

    6x=204

    We divide both sides by 6

    x=34

    That means the original width is 34 inches , and the original length is 68 inches

    Now we can calculate the original parameter

    2(34+68)

    2(102)=204

    The original parameter is 204 inches

    ------------------------------------------------------------------------------------------------------------------------------

    3-

    To solve this problem we need to solve a system of equations

    a:

    Let Sam's age be S , and John's age J , Therefore J=3S

    That means

    J=3S

    (J+5)=2(S+5)

    Substitute J with 3S

    3S+5=2S+10

    Move 5 to right hand side of the equation and 2S to the left hand side of the equation

    S=5

    Sam's current age is 5 years Therefore John's current age is 15

    ------------------------------------------------------------------------------------------------------------------------------

    b:

    Let the first integer be x that means

    (x+1)+(x+3)=132

    2x+4=132

    We move 4 to the right hand side of the equation

    2x=128

    We divide by 2

    x=64

    That means the integers are 64.65.66.67

    Let's check

    65+67=132

    The answer is correct

    ------------------------------------------------------------------------------------------------------------------------------

    4:

    a

    Let the first integer be x . Therefore

    2((x+1)+(x+2)=3x-34

    2(2x+3)=3x-34

    Distribute 2

    4x+6=3x-34

    Move 6 to the right hand side of the equation and 3x to the left hand side of the equation

    x=-40

    This means the integers are : -40,-39,-38,-37

    Checking

    2(-39-38)=3(-40)-34

    2(-77)=3(-40)-34

    154=120-34

    154=154

    The answer is correct

    ------------------------------------------------------------------------------------------------------------------------------

    b:

    Let the 2 numbers be x,y

    This means

    x-y=24

    x+y=88

    We add the equations

    2x=112

    We divide both sides by 2

    x=56

    We now know the value of x ,therefore we can calculate y

    56+y=88

    We move 56 to the right hand side of the equation

    y=32

    ------------------------------------------------------------------------------------------------------------------------------

    5-

    a:

    Let the small part be x . Therefore

    3x+6x+6=60

    9x+6=60

    We move 6 to the right hand side of the equation

    9x=54

    We divide both sides by 9

    x=6

    if the small part is 6 that means the large part is :

    y=60-x

    =60-6=54

    ------------------------------------------------------------------------------------------------------------------------------

    b:

    1-

    d=rt

    300=50t

    Divide both sides by 50

    t=6 hours

    2- d=rt

    300=70t

    Divide both sides by 70

    t ≈ 4.29 hours

    3- d=rt

    300=xt

    We divide both sides by x

    t=300/x

    4- d=rt

    300=(x+10)t

    Divide both sides by (x+10)

    t= 300/(x+10)

    5- d=rt

    300=(x-5)t

    Divide both sides by (x-5)

    t=300/(x-5)

    Hope this helped :)

  • ....
    Lv 5
    7 years ago

    1) a) 3x + x + 5 (3x) = 152

    3x + x + 15x = 152

    19x = 152

    x = 152/19

    x = 8

    tuesday --> 8

    wednesday --> 8*3 = 24

    thursday --> 8*15 = 120

    b) 5x + x + (4x - 3) = 167

    5x + x + 4x - 3 = 167

    10x = 167 + 3

    x = 170/10

    x = 17

    fred --> 17

    bill --> 17*5 = 85

    tim --> (17*4) - 3 = 65

    2)a) 5x + x = 168

    6x = 168

    x= 168/6

    x = 28

    width = 28

    length = 28*5 = 140

    b) 198 - 4 - 4 + 1 + 1 = 192

    2x + x = 192

    3x = 192

    x = 192/3

    x = 64

    width = 64

    length = 64*2 = 128

    Source(s): sorry, i couldn't go further than this. i hope this helped anyway :)
Still have questions? Get your answers by asking now.